Regarding android version, I think @boredsquirrel@slrpnk.net already gave a good hint. Currently f-droid version 1.21.0 supports android 6.0+.

According to f-droid basic URL:

NOTE: The Basic version of F-Droid Client has a reduced feature set (e.g. no nearby share and no panic feature). It targets Android 13 and can do unattended updates without privileged extension or root.

I don't see the target version varying between them, I found both to be 1.21.0 on Android (I have enabled unstable updates), and both indicate they support android 6.0+. So if you have LOS or plain android on a version 6.0 or beyond, f-droid should be able to install and work on them.

I use F-Droid since it comes pre-installed and with privileged extension set by default on LOS for MicroG, so I don't find it particularly appealing to install F-Droid basic instead, but if that were not the case, I'd go with F-Droid basic, given I don't set F-Droid to serve nearby devices on any phone, and I haven't ever thought of using the panic feature. I'm using LOS4uG 21, meaning android 14. with no issues, so perhaps 1.21.0 already target android 14, and not just android 13.

So I believe both, the basic and the not basic versions of F-Droid target the same version, and support the same versions, the difference is in basic with a couple of less features. But you can always take a look at the version, and there you can tap on the specific version to see what versions of android are supported.

Greetings !