For a 2-5 mile local ride, just about any style bike will do. The important issues are:

* Fit - You want a bike that fits you
* Reliable - A new bike from a bike store should be reliably built and correctly adjusted, and easy to get in your budget. It sounds like you don't have enough experience yet to have a strong preference.
If the bike is purely for local commuting and errands, used MTB bike are typically sturdy and cheap; this will depend local availability and your ability to judge condition/repairs needed.


I find the critical accessories are
* Lights - critical, especially if mild weather in LA makes it easy to bicycle even on short days in Dec and Jan. Get lights if you ride after dusk.

* Rack - Personally, I prefer a rack and saddlebag/panniers to a backpack. Either way, the bike will be much more useful if you can carry clothes for the gym or work, moderate amounts of groceries etc.