Additional to the Mint suggestions: Mint tones down the "Ubuntu-ness" of their default distribution, but it's still Ubuntu under the hood. LMDE is the version of Mint based on straight Debian skipping the Ubuntu "middle-man" if that sounds more appealing.
Can't speak to compatibility one way or another, though.
My computer is old and made of parts from well-known manufacturers. Everything in it is pretty well-known to the open-source community at this point, so that might well be giving me a huge advantage with regard to drivers and such. (Case in point, I have an NVIDIA graphics card and Intel i7 from the tail end of the era where people wouldn't advise you against getting either, and in fact might have outright recommended them over AMD. Yes, that old. Legacy proprietary drivers work fine for me.)