A linux mint 15 installer is only about 1GB, Netrunner OS around 1.6GB, Ubuntu 0.8GB, Zorin OS 1.6GB, etc.. You don't need a large capacity USB to run a linux. A 4GB USB flashdrive ($5) is more than enough (assuming you are not going to load videos and music on it). I did it already with NetRunner OS.
Cheers!