03 4.7 Quad Cab Comfortable Pulling Weight

Wife and I are buying camping property. New at campers and towing.
I have a 2003 4.7L Quad Cab. It is stock, except for the hitch I put on it.
What size/weight camper can I pull comfortably? Do I need to buy an accessories for my truck....IE: Trans cooler, sway bar, harnesses, etc...???
Can my transmission handle towing?

Your owners manual has all the necessary information.

I have an 04 QC 4.7. I tow a 7x16 tandem axle enclosed trailer for my business. I added helper springs to the rear and a large trans cooler. Trailer weighs about 4-4500. I tow with the o/d off and the temp rarely rises above normal; long uphill grades might get it to the half way point. With proper equipment, they are rated for around 7k, but I don't think I'd want to tow that much with it.