If you're not familiar with Linux, choose any of the Linux OS's that CorporateRecreation told you NOT to use. Because if you build Gentoo from scratch, you'll come out in the end with a nice Linux machine, but you would have forgotten much of the steps that got you there. If you don't know what any of the config files are called, it'll be too much memorizing all at once.
I'd recommend you use something like fedora and suse, but keep yourself mainly at the command prompt. Edit files, learn vi, awk, grep, sed, perl. That doesn't mean you don't install and use X. Without X and graphical web browsing, you'll probably get bored of your Linux machine too fast. X keeps you sane until and allows you to use Firefox to browse for online Linux help.