A couple of important tips, as I've been researching this for about a month now.
There are at least half a dozen major brands easily obtained.
Most will have one of 4 engine types: Briggs and Stratton, Briggs and Stratton ELS, Kohler Courage or Kholer Command.
They will be either 1 or 2 cylinder engines.
(There are of course others with Kawasaki or other type engines, but they're not in your price range.)
As a general rule, the basic engines are the Briggs and Strattons, found on most of the Sears types. Then there are the Briggs and Stratton ELS series (Extended Life Series). These are a better version of the the basic, with upgrades such as better valves, pump driven lubricatin instead of splash, spin on oil filters, etc. These are found on most of the Husqvarna types. After that are the Kohler engines. Most of the repair types I spoke with at my tractor dealer said the Kohler was superior to either B&S. The Kohler courage is the first level, and the Command series the upper level. These are found on the Cub Cadet series you see at Tractor Supply Company (that's where I bought mine)
As a rule, the 2 cylinder or "twin" engines will be quieter, stronger and less vibration prone.
I ended up with a Cub Cadet 1046 which I paid about 1500 for at TSC. That has the twin cylinder 23 hp Kohler Command, a hydro transmission like the Kubota, rock the foot forward or backward, no clutch, and drives like a car.
It also has a handy hose attachment on the cutting deck that allows you to wash the underside of the deck without lifting the tractor up.
Hope this helps at least describe your choices.
anthony