How can "2 miles each way and flat...." and "...I do live in a pretty hilly area..." apply at the same time?

Anyway, for a 2 mile commute (and flat) pretty much anything should do. An average non-competitive cyclist does 10mph, so you're talking about a typical ride of 15min .... so a "well fitted" bike, and a "fast" bike are probably things you don't need to worry about for now.

Pick something you are comfortable riding, and fixing. Perhaps an older 3 speed internal geared bike would suit you.