Not who you replied to but I haven’t had any issues with a 3000 series card and LTSC, but I only used it for a whooping 12 hours since I got the card (I do 99% of gaming directly on Linux) so take my answer with a grain of salt.
I might be missing something but can’t you just manually download the drivers from the Nvidia website on LTSB?
Keyboard and mouse for literally everything except things where using a wheel makes sense (ETS2 and ATS).
I can not use controllers at all. I can’t wrap my head around using them properly and pretty much all except one (ps3) hurt my hands after 15 mins.