Given what you want to use it for I'd look for a used hydraulic or PTO winch setup, but it would probably take a while to find one in your price range.
Second choice would be a worm drive winch, which you should be able to find (I got my used Ramsey RE10000 for $200)
Also, given what you want to use it for, based on many years experience doing exactly what you want to do, I'd use wire rope and not synthetic.
Tom Rowe
Four wheel drive allows you to get stuck
in places even more inaccessible.
62 88 reg
67 NADA x2
74 Air Portable - The Antichrist (tag 6A666)
95 D1 5-speed
95 D90 5-speed
97 D1 Automatic