Basically, you've got two camps in the Linux world at this point: Debian derived and Red Hat derived (I'm ignoring the semi-popular Gentoo and Slackware, for the time being - you can experiment with those later if you like). They both run the same kernel and desktop stuff, but they generally take a totally different approach to everything under the hood. As far as "consumer" oriented derivatives, you're most likely to run into Ubuntu (Debian derived) and Fedora (Red Hat derived). What you like ends up being to some degree personal preference. Both are reasonably decent at getting everything to "just work" out of the box.
I tend to prefer Debian's internals to Red Hat's, mostly out of familiarity, so all of my stuff is currently running Debian proper, Ubuntu (a Debian derivative), or MINT (an Ubuntu or direct Debian derivative, depending on what flavor you pick). Again, of those, Ubuntu is most likely to "just work", followed by MINT (not Debian edition), though I run LMDE and put up with having to occasionally fix minor things that break.
Unfortunately for new users, Linux hardware support tends to be "all or nothing". Either it'll just plain work out of the box (drivers included), or you'll be in for a world of hurt trying to make it work. Video cards are somewhat an exception to this, since both ATI and nVidia publish their own drivers that have to be distributed separately from the distribution. Ubuntu, at least, provides a nice installer wizard to grab the appropriate driver for your system, if applicable. Your best bet is to find a system known to work with your distribution of choice. Laptops can be especially problematic, but there are options out there. What "works" on your hardware may end up influencing your choice of distribution, so don't give up if the first one you try has issues. Such issues are not usually insurmountable, but they can perplex new users.
In general, the "core" OS works quite well, which makes it popular on servers. The desktop level stuff varies as to usability. Unfortunately, the GNOME guys all went and jumped off a cliff recently, and mainstream Ubuntu followed them with Unity, so you may do better with a KDE using distro (e.g. Kubuntu) if you find GNOME 3 or Unity to not be to your liking in terms of desktop shell.