As was said ride a bike you like and ride on the streets. A nice commuter bike can be had for $500-$1000 or you can find a good used bike for even less. Leave a good lock or two where you will park the bike daily and lock the bike securely.You will be riding your commuter lots so make it a pleasant ride.
Find the best route possible that avoids the roads you are worried about. If you must ride on those streets take a lane and ride like you are a vehicle. Once you get over your initial fears it is the safest and best way to ride in those circumstances. Chances are you can avoid those roads altogether with a little detour.
Craig