I wouldn't go as far as to say, don't care at all. Maybe just avoid overthinking. :)
Main differences of distros to keep in mind:
1) The default setup. (Desktop environment, already installed software, etc.) 2) Available packages. What software and versions of software are available to you without much hassle. 3) System upgradeability. (Rolling - always up to date, or a 6 month release schedule or something in between)
If I were to suggest something, It would be a variant of Arch called Antergos. You get an Arch linux that:
1) Is as easy to install as Ubuntu/Mint etc. 2) Good default setup selection. (Multiple desktop environments and more arguably the benefit of little bloatware) 3) It IS arch, just a extra enabled repository. (Antergoses own). This means you get the AUR (Arch user repository) that gives you easy access to packages that other distros might not have, although they are less reliable. (Though I have yet to see any problems in 2 years) AND the latest versions of much software. (Again can be bad, but in my experience I've only encountered minor annoyances that get fixed quite fast). BUT WAIT, there is more! It's rolling release. Always up to date. :)
In my experience the stability concerns of arch are a myth. If they do occur, it's not like you see crashing of your computer or massive graphical anomalies. Sleep might not trigger properly for a day or two or something like that. And rarely. But this is just my experience. :)
Antergos = Newest SW, rolling release, easy install, good default setup selection, AUR, the fantastic Arch wiki and probably more.
I am at the level where I can self-solve all my own problems, but if you are a beginner then stick with one of the major distros. Ubuntu and Ubuntu-based distros like Mint can't be beat for the sheer size of their community. Any problem you have, someone else has hit it before, they probably solved it too.
Arch Linux is a great learning experience, you really learn what the components of your system do, how they work, and how they interact together. Everyone should use Arch for a while as they become intermediate Linux users. Eventually maintaining your Arch system becomes a chore which eats into your "computer stuff" time.
Once you're at this level, you know what software you want, and you know how most of it works under the hood. Distros are now just different boot screens with different things pre-packaged and different things available in their repos. Use whichever distro provides what you need and gives you the least drama.
However, there are exceptions. There are experimental (though actually most are very much usable for real-world or even everyday tasks) distros with markedly different and more unconventional software stacks. Examples include Alpine, Morpheus, Sabotage, Void and NixOS. One should not be discouraged from trying those, not least of which is precisely to see other ways of integrating systems beyond the status quo.
It's frequently that case that new users of Linux think there is something to be gained by "trying" (and continuously reinstalling) different Linux distributions.
The reality is that the software that makes up Linux (iirc there are 30k packages in Debian) is generally available across all of these distributions to a greater or lesser extent.
It's all the same software with relatively minor changes made to it to fit into the particular distribution.
You can use almost any desktop environment from any of these.
The underlying system software is aligning quite a bit these days as well with systemd.
Stick with a distribution.
When something goes wrong, try not to reinstall but instead figure out the problem and fix it.
Modify the system to your liking and in the process actually learn the pieces that make it up.
Document, for yourself, the things you did so that you can be confident you actually learned something that you can reproduce.