http://www.madtux.org
Sells both Ubuntu and Knoppix Linux on USB pendrives. Both versions of these Linux OS installs boot up and run completely from a usb drive. I have the Knoppix version and have not noticed any performance problems. You may want to consider one of these options.
Another route is downloading DSL (Damn Small Linux) which has an option for you to install their lightweight version of Linux on a USB Pendrive by yourself. Included with the install of DSL is a lightweight webserver. I've tried this and the only difference between the Ubuntu and Knoppix versions is that the footprint is much smaller: 50 MB total for the entire DSL installation.
You can also consider running a LIVE distribution of your choice of Linux OS flavor. LIVE distributions are versions of the Linux OS that are runnable solely from CD-ROM and RAM memory. Once you've loaded up the OS, a RAM memory resident install is VERY fast. (Save for infrequent reads from the CD-ROM) LIVE distributions are cheaper (actually, free) compared to using a pendrive version which usually costs $40+ USD.