Well, distro choice is always very much a personal matter, so you
should understand that you just tossed a pretty loaded question out
into cyberspace.

That said, personally, I'm very much a fan of the Debian-style way of
doing package management, and both Debian and Ubuntu will do x86_64
just fine.  (I use Ubuntu on 32-bit systems myself - no no hardware
yet.)  At last check Ubuntu was running somewhere between 20,000 and
30,000 packages in the repositories, so that should satisfy your
package availability requirement, and started out as a desktop-focused
distro, which sounds like your kind of use (although it does great
things on the server end now too).

If you prefer the Red Hat way of doing things, OpenSuSE seems to
technically have some pretty good stuff, although I'm one of those a
bit irked by Novell's deal with Microsoft.  Meanwhile, Fedora is also
looking quite nice these days and is worth a look if you go that
route.

-- 
Tony Yarusso
http://tonyyarusso.com/