I'm also in a Great Lakes city. Our weather is similar to yours. The winds are the whole reason why I ditched my hybrid and switched to a drop bar bike for commuting. So I think it's a reasonable decision.

For a two-mile commute and your budget, your best bet is going to be something second-hand. Any touring bike takes a rack and fenders. Most cyclocross bikes do too. Entry-level roadies by the big three have eyelets and will fit fenders if you stick to 23 or 25mm tires.

If new is what you're looking for, you're pretty much restricted to entry-level. Each of the entry-level roadies by the big three have eyelets for a rack and fenders. The Trek 1.1 would work, but its $659 price just about shoots your budget. That's why I'm saying second-hand is your best bet.

Others are more familiar with second-tier makers. I'm sure there are a few jewels in there.

If you know your size and how to fit the bike yourself, there's the online option too.