Aurora Store - Install Google Play Store apps without a Google account - I recommend to switch all non-paid apps to be installed with this, and use an anonymous login if possible.
F-Droid: Install apps from centralized repositories (like a package manager) - I recommend to gradually switch all FOSS apps to be installed with this (not all Google Play apps can be installed with F-Droid of course). Other repositories can be added.
Obtainium: Install apps from the 'releases' page of the app's Github/Gitlab - I prefer this to F-Droid if possible, but there is little difference and it is slightly harder to set up, so I don't recommend this initially.
And last of all, installing an APK manually from the internet (works similar to an EXE installer).
Each of these options should work on all Android distributions or ROMs.
What's your opinion on APKMirror? I have a fire tablet for which I've been trying to get apps that aren't available throug the Amazon appstore. I just want to make sure that I'm not loading malware.
I think it is relatively trustworthy, and I have used it to install Youtube to be patched with ReVanced. I would still be a little cautious downloading a apk from any website, but apkmirror might be the safest option due to it's popularity. but still use F-Droid or similar if you have the option.