I like the Kenda small block tire, it handles pavement, gravel, dirt and sand well. It's a little wider at 2.1 or 2.3, though.

If you have 6 sprockets in the rear, then I think you'd have to be dealing with a freewheel, which means you'll need a new wheel with a freehub body if you want to move up to a 7-10 speed cassette. You'll have to check the rear dropout spacing as well