You are VERY smart for budgeting beyond the bike. Take a look at cross bikes. They are a good combination of versatility and speed. They can take wide MTB-sized tires or narrow road bike tires, depending on your preference.
The
Surly Cross Check will leave you half of your budget (depending on the components) for the extras. You should also take a look at the
Surly Long Haul Trucker, which is designed for touring. Both can handle the rack, fenders, etc. you will want for commuting. (I have the Cross Check, and love it.)
If you're riding on LA streets, don't get narrow tires. I'd say 28's are the minimum. The wider the tire, the smoother the ride. But the wider the tire, the more you have to work. You have to decide what's important. Stay away from knobbies, they will make your street rides harder. Tires with little or no tread patterns are the best for city riding. Either get tires with kevlar liners or put kevlar liners in the tires.
Don't cheat yourself on lighting. Get at least a 10w Halogen with a battery that will last several commutes between charges. Also, get a back up light--even a be-seen LED is better than riding dark. Get two rear blinkies. One attached to your bike (mine is attached to my seat bag with zip ties) and the other to your helmet (I clip it to the strap). You may also want a reflective vest.
Get a frame pump and seat bag with all the stuff needed for emergeny repairs--spare tube, patch kit, tire levers, multi-tool, energy bar (in case you bonk), chain tool, spare batteries for your blinkies and LED, etc.
Finally, get a copy of a good bike maintenance book. I like Zinn and the Art of Road Bike Maintenance (he sells one for MTB's too). Then get the basic tools the book recommends. When something goes wrong with your bike, buy the tools and the parts and figure out how to fix it yourself.