I don't have an HP myself, but my university (like most others) offers laptops that were extensively tested in multiple aspects, one of which was Linux compatibility. However, those are primarily business-oriented models (ProBook, EliteBook). (AFAIK, even HP offers some of them with pre-installed SUSE.) I'm not so sure about the "Home user"/"Media PC" segment.
Anyway, there are so many different drivers nowadays that you can get almost anything to work, but it might be quite tedious, and it's not really fun unless you enjoy fumbling around with kernel modules.
The only reliable way of finding out what works and what doesn't is taking a Live CD to the store and trying things out.
And now to answer your question (:P), I don't think it really matters. Any distribution which provides a fairly wide range of up-to-date packages is fine. Others will work too ofc, but you'll hate yourself every time you have to compile dependencies manually ;)
TL;DR: YMMV.
Anyway, there are so many different drivers nowadays that you can get almost anything to work, but it might be quite tedious, and it's not really fun unless you enjoy fumbling around with kernel modules.
The only reliable way of finding out what works and what doesn't is taking a Live CD to the store and trying things out.
And now to answer your question (:P), I don't think it really matters. Any distribution which provides a fairly wide range of up-to-date packages is fine. Others will work too ofc, but you'll hate yourself every time you have to compile dependencies manually ;)
TL;DR: YMMV.