I would first sign up for the Lake Erie list here on Sailnet. Look in the archives you'll get lots of information on Lake Erie Sailing.
There are many boats that would fit your description: My first choice although I don't think it would be in your dollar range is an S.2 7.9. Only because I owned one.. Great weekend boat, fast, strong, will hold up to Lake Erie Chop.
Lake Erie is very shallow but with 99% of the trailerable boats you should be ok. Other boats Oday, Catalina's, hunters all live pretty well on Lake Erie. With your price range I would be concerned more with the boat than with the make.
If you look hard you could dig up a gem...expecially in the good shape but not clean category. Some folks think since you'll only putting out a few thousand dollars you shouldn't expect clean.