It depends on what you want to do. If you just want to introduce yourself to the fun, fun (no sarcasm, REALLY!) world of video editing, Premiere will definitely let you learn the ropes. The thing is that on the surface, video editing is largely the same, no matter what program you use. They all have a timeline, a bin, a few audio tracks, and a way to output what you need. That said, if you ultimately want to take the next step and maybe find work in the field, you
need to know either Avid of FCPro.
Avid offers a barebones version of their editor for free, it's good for learning their specific software, where everything is, etc:
http://www.avid.com/freedv/index.asp
Final Cut Pro is also great, despite it's sometimes unabashed preference for Firewire (but maybe that's changed, I haven't used it in about 2 years.)