Buy a small tractor and pick up a used finishing mower to go with it. I have cut a lot of property with a finishing mower and the yards always look great. A small tractor will last longer than both of us. Ten thousand times more dependable than a lawnmower and the attachments like a bush hog make it an all around working machine. Many used small Ford and Massey Ferguson tractors can be purchased in your price range. Hope this helps.
BTW-I bet you can keep the tractor ten years and get all your money back from it. Try doing that with a lawn mower.
^^^^^THIS is the way to go and what I do UNLESS a you have a lot of stuff to trim around in your yard. A grooming mower will cut like a lawn mower deck BUT when you turn to go around something (tree, bush, etc) the mower is swinging AWAY from what you're trying to trim around. With creative landscaping this can be overcome and in the long run is a much cheaper method.
I have a Tractor, but use my ZTR to cut a mowable 2.5 acres of my property... The tractor is Harder to maneuver in and around fences, shrubs, ditches, propane tanks, water wells, raised gardens, landscaping and etc...