For rain gear check out a local sporting goods store. I bought a Field & Stream rain jacket and pants for about a total of $60 at Dick's. For 2.5 miles you don't have to worry much about breathability. You can also check out Nashbar.com. They have some rain gear I might look into purchasing.

For your distance any bike will do. In time you might grow to enjoy it and then look for something that suits your needs better. Like another poster mentioned, don't over complicate things.

Besides rain gear look for a good lock and learn how to lock your bike properly. Sheldon Brown's site has some good information. After that think about visibility both passive and active.

Good luck and enjoy.