If traveling alot, then get the MBP or MBA. They are designed for more rugged, portable, use than a mini. If by traveling alot you mean you go to school, go home on vacations, then back to school, I guess you could use a mini. Personally, traveling with a mini, keyboard and mouse would be slighlty annoying, but it certainly can work. If I were going to opt for that solution, I might go for an SSD instead of a traditional hard drive, to minimize exposure to jostling around, which of course raises the price more.
Monitors have one wire that plugs into the mini, however, if the monitor requires a DVI or VGA port, you'll need to buy a separate adapter from Apple.
On price, make sure you're looking at the Apple educational discounts you are eligible for.