Welcome to Linux!!!
64-bit Linux is really nice, but does have a few draw backs still. Mostly with third party stuff, Adobe flash and reader applications along with some other things (no 64-bit support yet). Some (like me) choose to run the 32-bit versions of fireox and mplayer as a workaround to these minor issues.
By default getting the 32-bit versions installed are not hard, one just needs to specify the version. With firefox one removes the 64-bit versin and installs the 32-bit version;
yum remove firefox
yum install firefox.i386
For mplayer (nice for watching videos on the Internet and locally) one again specifies after adding a third party repo like freshrpms.net ( http://zod.freshrpms.net/
yum install mplayer.i386 mplayerplug-in.i386
The mplayerplug-in works with firefox and mplayer so one can watch Internet videos.
The choice is yours, many use the 32-bit version and many use the 64-bit version. if you are just starting out then the 32-bit version is the better of the two choices. Any of the Linux versions you mentioned are god for beginners. Since you like fedora Core best then use it, myself I prefer the more stable choices of RHEL or CentOS. Both are almost exactly like Fedora Core except they are more for stability instead of leading edge, CentOS is a freely available version of RHEL. Both RHEL5 and CentOS5 are based on the work done for Fedora Core 6.