These days Linux is not fussy about hardware, except for some video cards - usually older ones. The best bet is to search on-line for the name of the card and "linux" and see if you find lots of cries of woe! Your printer is more likely to give trouble than your computer: some manufacturers, like HP, offer drivers for almost everything; Lexmark generally only support their laser printers.
Choosing a distro is a very subjective thing. I always advise starting with the GUI, which you get to choose in Linux.
Gnome: looks a bit like a tablet (or Windows 8). Ubuntu do a nice implementation.
Unity: looks like a giant phone. Only available from Ubuntu.
KDE: lots of eye-candy and very versatile (and you get a proper menu/start button). PCLinuxOS and Open SUSE are the experts here.
Xfce: traditional interface (more XP than 8). Antix MX and Xubuntu are both good.
Mate: also traditional. Mint is the best version.
The distros I've mentioned are all high quality. You can read reviews via their pages at
I don't recommend Fedora - often very experimental - or Mint's Debian Edition - may give problems when updating. Theya are both nice if you know your way around, but they're not for beginners.