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What can I expect to change about how I write python on my Mac after I install conda?

Background
Currently, I have Python 2.7.17 and Python 3.8.1 installed on my Mac (v 10.14.6). Both Python versions were downloaded directly from Python.org using a "macOS 64-bit installer" .pkg file, in late 2019. Both were installed here:
python2: /Library/Frameworks/Python.framework/Versions/2.7/bin/python2
python3: /Library/Frameworks/Python.framework/Versions/3.8/bin/python3
Currently, I use only pip (either pip2 or pip3, depending) to install python packages, which are saved here:
python2: /Library/Frameworks/Python.framework/Versions/X.X/lib/python2.7/site-packages
python3: /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages
I am about to begin an online course which requires that I install miniconda in order to install the packages that I need for the course. But after having a very bad experience having Anaconda installed on my machine years ago, and it taking me months to remove it and re-create a clean Python install, I am nervous. I don't want my machine to become a mess again, rife with error messages that it can't find this or that python version or this or that python library.
Question(s)
Assuming there will now be multiple installations of Python on my machine (in addition to the versions that I already have, since I believe yet another version of python is installed along with conda), and there will be new places where python packages will be saved, what can I expect to change about how I write python after I install miniconda?
Is there anything I will need to do differently from what I am doing now when I write python code?
How can I ensure that everything remains working and compatible and I avoid the fate I suffered many years ago?
Happy to edit/clarify this question per user suggestions. Thanks!

Use conda environments and install Python into those environments. This ignores, by design, the versions of Python that are installed at the system level. Also, what's installed into environments (other than the one you're in) is ignored. As somebody who uses conda for all Python development, I don't even know what I have installed in /usr/local/bin/ or other places. Everything is in /path/to/miniconda3/envs/env_name_n. You don't have to uninstall other versions of Python you have elsewhere; the point of environments is to keep everything isolated.
What can I expect to change about how I write python after I install miniconda?
Is there anything I will need to do differently from what I am doing now when I write python code?
Use conda environments and use conda as your package manager. For almost every major project, it nearly a drop-in replacement for pip. Outside of managing dependencies, not much changes.

So many pythons, which do I need?

It seems I have several Python versions installed on my Mac (High Sierra). Do I really need more than one each of Python 2.7 and the most recent Python3?
I am primarily concerned about confusion when adding modules to the environments.
Here are the python executables I can find, excluding symlinks. Do I need them all? Does Apple need one version just for the OS? (Maybe that's Ruby I'm thinking of._)
/usr/bin/python
/usr/local/Cellar/python/2.7.13/Frameworks/Python.framework/Versions/2.7/bin/python
/usr/local/Cellar/python/2.7.13/bin/python
/usr/local/Cellar/python/2.7.13/share/python
/usr/local/Cellar/python/3.7.1/libexec/bin/python

On MacOS, you need to have the system-installed Python 2 in /usr/bin/python because some system functionality depends on it.
If you have other versions installed via Homebrew or etc, that's strictly optional. For developing code in Python, definitely install a recent version of Python 3; you should not be developing new code in the legacy version 2. It will run out of support in a year or so, and many important third-party libraries etc have already abandoned support for it.
If you do need to maintain Python 2 code, having a Homebrew version of the most recent Python 2.7.13 is probably a good idea. The system /usr/bin/python is at version 2.7.10 as of MacOS Mojave; and if we extrapolate from Apple's update policy history for third-party open-source software in the system, it will probably remain there for many years.
Homebrew is just one of many ways to install additional Python versions, but since this is what you seem to be using already (as indicated by the /usr/local/Cellar paths) I will not go into alternatives.
For switching between versions, virtualenv is the common baseline, though there are many add-ons like pyenv etc which add convenience features or alternative models for switching between projects which require different versions of Python and various packages.

Note: this answer might be primarily based opinioned.
First, in macos, I encourage you to use brew to install python. So, if you want to instal Python 3 run:
$ brew install python
Probably it is already installed, so to update it run:
$ brew upgrade python
This will upgrade to the latest version of Python 3. In general, if you start a new project you should use Python 3. Remember that Python 2 will be deprecated at the end of this year 2019.
Second, I highly recommend you to use virtual environments to avoid having issues with dependencies. You can create a virtual environment running:
$ python3 -m venv .ven
This will create a virtual environment in .venv in your current working directory.
As an alternative you can use pipenv to track dependencies too which I also encourage you to install using brew.
$ brew install pipenv
Then you create a virtual environment running:
$ pipenv --three
Keep in mind that you will have two versions of Python in your machine python which is Python 2 (installed by default in your machine) and python3 which is Python 3. Then, if you want to run Python 2 just type python, while if you want to run Python 3 type python3.
Finally, you can also keep track of several python versions using pyenv. This is very useful if you need to use multiple versions of Python for example Python 3.1, 3.2, 3.3..., 3.6, 3.7.1, 3.7.2, 3.7.3, etc.
This is what has been useful in my experience using macOS. You could also use Docker to completely isolate your environment, but probably the first two points is enough if you are a beginner.

While Python 3.x is what python solutions should be implemented in today, many existing python applications, modules, etc, are implemented and maintained in 2.7 or lower. Sometimes you'll find multiple versions of python on your computer because applications you've downloaded in the past had you install them so their application would work properly on your machine. As long as you don't want, or need applications that may depend on past versions of python, you can update to the latest one and delete the old versions.
If you are planning on developing in python, and you can use the latest version, you should definitely do so. If you rid of the versions of python on your machine, applications, modules/scripts, etc may not work or function properly.
Python comes pre-installed on Mac OS X, but it is not required to be on your machine for your computer to function, just the applications that may be on your machine that may use Python.

Three versions of Python?

In case it is relevant, I am using Ubuntu 16.04 LTS. I went to install some software (Jupyter Notebook) which uses Python, and the recommendation was to either use python3 install if I have Python 3, or python install if I am still using 2.7.
My Ubuntu installation came with both. python --version returns 2.7.12 and python3 --version returns 3.5.2. However I also know that there is currently a Python 3.6 out there, which I installed... but it appears to use its own special reference python3.6 --version which returns 3.6.4, whereas I had expected it to upgrade/replace python3 so doing python3 --version would return 3.6.4, but nope.
I'm not sure what the correct approach is here because apparently I shouldn't be messing with the Python versions that come installed since the OS may rely on them. At the same time it seems strange to install software that calls for Python3 even though it's going to be using 3.5 rather than 3.6.
Am I overthinking this? Is it expected behavior to use python3.6 specifically for 3.6-related features? Or do most people re-alias python3 to redirect to python3.6 instead? What about pip? pip3? Is there a pip3.6? I'm not entirely certain how I should be thinking about all these different Python installations.

You may want to use virtualenv so you can control your python environment, it's good practice. With virtualenv you can specify which version to use and your libraries are installed only for the project that needs it.

You can use python2 and python3 alongside just fine. However, if you want to use different minor versions of the python, for example 3.4 and 3.6, you have to set up virtual environment for each version. Look for the virtualenv or other solution.

How to use and install all the libraries of Python3?

Using Ubuntu 16.04.
I was doing development in Python2.7, although recently moved to Python3.5, both of which come by default. The problem is, I find all the python libraries have to be reinstalled or downloaded for the next Python3. Also, the behaviour of Python seems weird because to execute the same script in python3, I have to enter in terminal
python3 script.py
which is different from other applications where I do not have to give the version number. Anyway, the questions I am trying to find answers are
To what extent are the libraries, packages (such as pip etc.) shared between 2.7 and 3.5? Or do I need double installations (and double the space) for everything now? A bit space limited in my old laptop.
Most of the installation instructions and commands I find online do not specify whether they are for 2 or 3. Given that I have two versions, how do I control/make sure they go to 3.5?
Is it advisable and possible to completely remove everything related to 2.7? Can I keep working with 3.5?

The first thing you need to know is that all official libraries and python tools for python3 got the "3" character to separate them from the previous versions. So, you need to use pip3, and not pip, python3, not python, and the packages are called python-pygame, not python-pygame.
So, to answer to you in order:
Yes, the you have to double the space needed if you decide to use both python2 and python3
Usually, if in the tool name there is 3, it is for python3, and if not it's for python2
Python2 and python3 are completly indipendent (different path, indipendent versions, etc.) so having python 2.7 installed doesn't affect python3 BUT since python 3 is the next version of python 2, it makes it obsolete (in my opinion) so if you don't have enough space for both, keeping python2 is absolutely not needed nor useful

If you want to control your python execution then you have various method or techniques:
For downloading packages according to version
You can use pip{version-name} to download the libraries. Like if you want to download library of python 2.7 then write
pip2.7 install package-name
for python 3.5 then use
pip3.5 install package-name
For execution of program:
If you want to execute the program accoridng to you choice of version then just use
python{version-name} script.py
eg:
python2 script.py
python3 script.py
or you just write down the path of your python version on the top of script. Please refer this for more details:
Why do people write #!/usr/bin/env python on the first line of a Python script?

Brews Python 2.7.7 shows up as 2.7.5

I installed a fresh version of Python via
brew install python
Also
brew info python
tells me that it is at version 2.7.7.
I seem to remember that the python OSX Mavericks ships with is 2.5. So that
python --version
gives me 2.7.5 makes even less sense.
Also
which python
/usr/local/bin/python
should be the Homebrew version, correct?
I'm lost. Does anybody know, why my Python isn't version 2.7.7?

You have to explicitly tell brew that you want to switch to the version of python you just installed. To do that, type:
brew switch python 2.7.7
in your command line. This may not work if the version you installed is actually 2.7.7_2. In that case, just replace 2.7.7 with 2.7.7_2 above and run it again. Once this is done, you'll have to reload your environment to pick up the changes.

Python from my experience doesn't do an upgrade in the sense we would like it. Basically it will install python but not overwrite the old version. If you look in your main drive you will prolly see Python 2.7.7 and Python 2.7.5
usually in Windows its: C:\Python27
It doesn't really show the last digit (which from my knowledge refers to bugs fixed in the version), so it may overwrite unless it is an entirely new version. '
But I would check first if you have two files of Python. If you do then change your PATH variable environment to point to the latest and delete the old version.
That's my suggestion but I use Windows and pip install, so hopefully it is not too different.