You're in a good market to find something great. Whatever you end up getting it would be wise to frequent one of those coops in your area. They'll teach you basic maintenance and they probably have a good parts bin for you to do modifications and repairs as they come. Rarely does whatever you buy work exactly as you want it out of the box, and if it does it doesn't stay that way forever.

Your commute is also not necessarily a hilly one. You'd probably be taking the LA River path most of the way so unless you're taking a detour for exercise you don't really have to scale Griffith Park or summit any mountains.

Get a basic road bike that's more cromoly than not and whatever gear set it comes with will probably be adequate. Just make sure it fits. After that I'd definitely invest in some rack/pannier setup because riding with a backpack is sweat city and more tiring than riding with your books attached somewhere on your bike.

The Schwinn looks too big for you, the Fuji a tad small. Making a slightly smaller bike fit larger is easier than making a slightly larger bike feel smaller in my experience.