Being a Linux user for the past 13 years, (starting when I was 6), one of the biggest brainf***s you could do is start with a UNIX system (the only exception being Mac OS X - which is a Darwin/BSD UNIX core), especially when you are coming fresh from the Windows world of computing.
I change distributions, practically, every few months, and I have finally settled on
Debian. It's small, easy to setup (my brother, who doesn't know the difference between the CPU and RAM was able to successfully install it without any of my help), and it doesn't have ridiculously bulky packages and clunky dependencies like the RPM-based distributions.
Spend a few, comfortable years (or a few fast-paced, accelerated months) learning conventions inherent in Linux; most importantly, learn to use the command line. Learn about logical command chaining, and how to - essentially - control the computer from the command line (setting up/monitoring daemons "servers", administrating users and processes on and off networks, man pages).
After you're comfortable, with that, you will need some handbooks for the UNIX (*BSD or Solaris) way of things, and you will be set to go. There are subtle differences between LSB (Linux Standard Base) programs and UNIX programs; keep in mind Linux is more so a giant collective of thought, like the Borg, whereas the UNIX world is essentially multiple mimicries on the same entity by huge corporations (SCO, Sun, HP, etc.).
For example, to list all running processes from all users on a Linux system:
$ ps -ef
And on a *BSD system, it would be:
$ ps aux.
Subtle differences like that.
As for my opinions on other Linux distributions, here goes:
Gentoo - don't waste your time. It's trim, but I don't want to spend 2+ hours installing an OS. I could see it being a good tool for learning the short and curlies of a Linux machine from the inside-out, but after a while, you may find that waiting 20+ minutes to install, erm compile, Firefox isn't worth the wait.
Fedora, Mandriva and other RPM-based distros - Too bulky and too clunky. They're perfect distributions for setting up on workstations where is strictly for end-users in, say, an office situation where the users need to do work, and aren't learning about Linux systems. Also, as far as system configuration goes, they hold your hand something fierce.
Debian, Ubuntu and other DEB-based distros - Really good. Ubuntu is perfect for the new-to-Linux-from-the-Windows-world type of person (such as yourself). It aids the user in things such as system configuration and installing/removing packages (programs), but doesn't pamper you to the degree most RPM-based distros do; it provides adequate control without too much abstraction. Once you get comfortable with Ubuntu, I suggest you give Debian a shot.