An Ariens IKON-XD is $3673, which is pretty close to your budget, has a serviceable transmission, and from what I can tell reasonably well built. It comes with a Kawasaki FR600. I think it’s kind of where the more robust mowers start. Once you go much below that, it’s not that they won’t work, or even give you decent service for a while, but they are hard to repair, lighter weight, and not built to last as well.