If you're plan on putting the zines together yourself, try to print as cheap as possible. I printed with Kinkos for my first zine and it was a nightmare. The quality wasn't good, the prints weren't aligned on the front and backs of the pages so I couldn't actually use the prints at all because there would be no way to trim them down. Then they gave me a hard time when it came to getting a refund, I cried. I was later told "crying in a kinkos is a rite of passage" by my cartooning mentor.
If you have to print somewhere, try to use a local place that will work with you... or Staples, they tend to be a little more helpful. Every Staples I ever got prints as was really willing to do reprints and color correct if there were any issues. But with zines, since people expect them to be small and handmade, you can use a home printer or school printer or print at work (if your boss doesn't mind). That way you can be hands on and make sure the prints are right and also hopefully save a little money. I print the interior pages on my printer at home and then get the covers for my zines done at a local shop.
If you plan on doing a big batch or more zines in the future, you can invest in a long-neck stapler and a paper cutter. When I was in school I just used the tools they had available, but after I graduated I got a really cheap little desktop guillotine paper cutter that I think was made from scrap booking and a long stapler. It's super time consuming and tedious putting together comics, but it's easier with the right tools.
For bigger projects I use comixwell.