What everyone else said about cheap ZTR's.
An acre with some trees would have me buying a regular lawn or garden tractor made by one of the following: Cub Cadet, John Deere, or Simplicity with a 42"- 48" deck.
Most brands make a cheaper "box store" variety. This may be suitable for your needs if you don't plan on adding attachments beyond something like a waggon or seed spreader. They are "consumer grade" construction, and you'll be lucky if they last for +/- 8 years or so without major parts replacement. Definitely the cheapest way to go for someone on a budget though.
On the other hand, the dealers will carry the heavier, better built GT's (garden tractors) with thicker welded frames, commercial grade engines, shaft drive, heavier tranny that's serviceable, greasable zerks, and better build quality/components all around. These tractors will have a ton of different attachments and will last for MANY years if you take care of them. They do cost though. Expect to pay not hundreds, but thousands more. It's worth it to some people. It was worth it to me.