Welcome to the forums! 2gb is plenty of space to create a "Live USB" of any distribution available on CD. (DVD-sized distros won't fit.)
Here is a comparison of the most popular distros: http://distrowatch.com/dwres.php?resource=major
If you have never used Linux before then I highly recommend Ubuntu. They have a good USB installer (with a "persistence" feature to save your documents and settings) and a very friendly community at ubuntuforums.org.