This is my winter bike:

http://www.bikeforums.net/showthread.php?t=482897

It rains nearly every day from November to May here, and this bike has served me well. I've recently added Schwalbe Marathon Supreme tires, which are supposed to have excellent grip in wet conditions.

Leave $100 in your budget for a comfy saddle, but if you're going to ride in the rain a lot, ask pointed questions of the hordes who will shortly recommend a Brooks B17. I use a Specialized Avatar, and it's pretty good. The Specialized Body Geometry saddles come in multiple sizes, which is key to comfort. Get measured.