depends whats in the trailer. I have a 2500 chevy 6.0 and use it for my lawn truck and I also tow a 26' camper. This is a small-ish camper compared to what I could pull with that truck. But it's comfortable towing that size camper loaded around 7-8000 lbs. Now, I see guys rolling in to campgrounds towing 30 footers with Ford explorers, or similar. not the smartest thing to do, but it does happen. So your 1500 would certainly pull a 20' enclosed trailer as long as you're not crazy heavy. So don't load it up with 5 zero turns, a few walk behinds, a compact tractor and a race car. if you need to fill that size trailer, def go with a 3/4 or 1 ton. might consider a WD hitch as well.
As for trucks, I can only speak for the 6.0 and 8.1 gassers from Chevy. I have the 6.0 and it's OK, not great but it does fine, never overheats, never complains, just is a bit underpowered on hills sometimes. no issues with my lawn rig tho. it also is thirsty on the gas. towing the camper I get around 7-8mpg. Now, I've used a friends 8.1 chevy before and that thing pulled every bit as well as my old dodge cummins did. I wish Chevy still made that 8.1 it got the same mileage as the 6.0 and had tons more power. But I don't think you'd be disappointed with the chevy 6.0 with a 20' trailer unless you're in the rocky mountains.