Well can't hurt to go big, mud has massive suction especially on larger tires so I would look to go bigger than 8000. 500 bucks will cover a nice winch I got my 8500 Rugged Ridge for 300ish shop around I have heard a lot of good reviews on Harbour freight winches and they are pretty cheap.
These go on sale quite often.
Best bang for your buck Warn
A winch is something that sits 90% of the time and you only need once and a while, but when you need it, it has to work. Most important thing is PMS it. I operate mine once a month, check connections to ensure they are free of corrosion, and a big thing is most winches have aluminum parts and stainless steel bolts this is very bad because they are in different metals and will corrode really fast and basically become welded. I removed all bolts coated in anti sneeze and replaced I check those about every 6 months. Even with a cheaper winch if you take care of it then it will last a while. I have had my winch as long as I have had my JK getting clost to 2 years and used it maybe 3 times.