If you get a heavy duty 1/2 ton truck you can do just fine.
My sister has a large Hawk 2 horse w/ dressing room that she uses my parents dodge 1500 w/ a large V8 motor in it and a tow package
Obviously a diesel is nicer for towing but if you're just going to the occasional show and trail ride probably not worth the extra expense of purchase and upkeep.
As far as short vs long bed, you can get away with a short bed for a bumper pull and for a lot of goosenecks, just have to either get an offset hitch or a gooseneck with a narrower front end
My current truck is an 08 chevy 2500 w/ diesel and I love it, but I tow daily
So easiest to find a truck or a few trucks and ask...sorry to throw a wrench into things, just my 2 cents