Linux can run easily on that.. the pratical lower limit is a 486 with 16 megs of ram, but the bottom feeders can struggle thru with a 386 with 8 megs and extremely painfull experiances with a 386 with 4 megs of RAM..
And you could use X windows with that two, but you ain't gonna be able to have non of them purty apps... Like mozilla or KDE/Gnome stuff...
I recommend using a minimilist distro such as Slackware or Debian, or OpenBSD if you feel adventurious. If you are not sure you know enough to use those versions of Linux you can make do with more user freindly versions such as Red Hat if you make sure that you try to do a minimilist as a setup as possible. By using windows managers such as IceWM, Blackbox, or TWM, you can have pretty snappy response with from you box without thrashing the snot out of your Harddrive...
Athough for the most usefull learning tool possible I'd stay away from X and use command line stuff... If you want something nice setup a ssh server on your box and use the combination of Putty.exe (windows app)/screen (nice terminal session manager) on your windows box.. That way you can have tutorials and references going on in the background in you windows desktop but have a nice interface with your Linux computer. You could use the normal telnet stuff built into your DOS stuff, but I find the combination of ssh and putty.exe to be very superior...
If you want to have a purely unix experiance, learn to use vi (or emacs) well, use links or lynx for a text based webbrowser. Also if you have to type stuff by looking at the keyboard constantly or your a hunt-and-peck type of person, It is a very usefull thing to know. My vi sessions were almost unbareable until I was able to train myself to type without looking at the keyboard (well mostly ) Now I've gotten up to about 40 WPM and now it seems like a pain in the butt when I have to reach all the way over and use the mouse when typing something out or to make corrections, it just slows me down. My linux bash experiance increased in quality drasticly when I learned to type well. (or well enough)....
Plus they have a modified version of links out there that support running graphics in your vid card's frame buffer so you don't even have to use X windows at all to get gifs and jpegs to appear on your terminal (only works from the actual computer, not thru a remote session)
I have a old proliant server box that has 80 or so megs of ram, and a 486 that has been replaced with a pentium overdrive chip (about 80 mhz). It runs my main ssh/ftp server and at one time I had nfs/cups/ftp/apache/samba services all running at one time with no slowdown noticable when using a terminal or uploading/downloading files over my cable modem line.