I'd suggest a CVA Wolf - it's gotten good reviews and is very inexpensive. It's a break action that is easy to use and easy to clean. It also pretty accurate. I don't own one, but I own another CVA bolt-action that I like a lot. Nothing special, but it gets the job done and is very accurate. The Wolf should be easier to use & clean because of the break-action design.

Traditions is another company that makes decent, affordable ML's. The Traditions Tracker costs around $100, or slightly more and is a good rifle. 2 guys I hunt with have Trackers and they shoot really good with 240 grain XTP's - they've taken numerous deer. The Trackers are a little harder to clean, though.