I've been sailing my whole life on lake erie and on open ocean, and my advice is to get something with a keel. The Northern great lakes are really suspectible to line squalls (where the wind goes from 0-40kts in seconds b/c of a huge low pressure system), and every time I've experienced them, I've capsized. There's nothing you can do about it in that much wind.
If you've got a keel, you're pretty safe, because of the lower center of gravity. Also, without a keel, the wind will tend to overpower you even if you flatten/reef the sails, and it gets impossible to go upwind b/c of wave action, unless you're a really good sailor. A J-24 or 22 would be a great boat to do a trip in, or something similar. They're pretty stable (I have seen a few broach though). The cost could be really prohibitive. It depends on if you're doing open water-remember, the great lakes are big enough to be considered blue water sailing. Having a nice little outboard is nice, too. A 2hp or something. Having a spinnaker rigged up is great for downwind runs, which you'll be likely to get a lot of.
I could go on and on about this, but I don't really have the time. Having a handheld GPS is a really good thing if you're going offshore too, unless you're really good at dead reckoning, which no one is these days.