TinyMe will run fine on that. It's a stripped down version of PCLinuxOS. Puppy will work, Damn Small Linux will work, and there's a couple of others out there whose names escape me.
Most Linux distros need at least 256 RAM to load and run, later machines need later kernels and more memory. Older machines like yours need older kernels.
I've got a 233 laptop with 64 megs of ram that will not run any Linux distribution I have, but will run Windows 98 like a champ.
For an easy installation, I would recommend the Linux book for non-geeks 3rd edition. I would suggest getting the book and reading the first few chapters first to orient yourself with a new way of doing things, compatibilities, pre-install info, etc. Includes disc with install and live functions if you haven't burned an iso image on a CD yet. All the info you need to install codecs to play MP3’s, other files, radio streaming, DVD playing & Backup, Real Player, etc are in the book which covers a complete functional install.
http://www.amazon.com/review/product/1593271808/ref=cm_cr_pr_recent?_encoding=UTF8&showViewpoints=0&sortBy
Ubuntu (Hardy Heron) 8.04LTS came out mid year or so 2008, and it is supported 3 years.
I can make these suggestions as I used the book to install 8.04 on two Dell D600 laptops dual boot with xp, with no knowledge of Linux. After about 4 months use I usually use the Linux Ubuntu about 75% to %25 XP.
The Linux system doesn't seem to require the maintenance XP does or defraging and constant anti virus worries. I spend all the time I used for those things in just using Linux.
BTW, for the Linux experts out there. I'm am lost when it comes to setting up wifi drivers for a card, is there a tutorial out there that shows the proper procedure to use when getting a wifi card working? Or what to do when the Network Mangager doesn't show a wireless signal. TIA