Which Rig?
I have a GMC long bed, extended cab with 410 positraction/limited slip gears, auto transmission with tow/haul mode, 6.0 L gas engine. I have always had good luck with chevy/GMC vehicles (usually they are still working past 200000 miles) and bad luck with fords (they start breaking down at 50000 miles). Dodge seem ok mechanically, but my dodge bodies fall apart early. This is strictly gas, and just the way it has worked out for me. I don't claim that any of these brands are intrinsically better or worse in general, just this has been my experiance.
If you are going to tow a 5th wheel, then the long bed will save you trouble; for towing trailers, the short bed may do. The extended cab is very, very useful; it can carry stuff protected from the weather and other people, and most importantly, you can incline the front seats
. I'd never go back to a standard cab truck. If you often carry people back there, then the crew (4 door) cab may be of use.
My truck is a 2500 HD, which is a 3/4 ton on steroids, or a wimpy 1 ton. It is supposed to tow 9200 lbs, I think, making it the highest rated 3/4 ton. It handles 6-7000 pounds very well, and with the right engine could probably approach its limit without serious worries. The small block gas engine, though, is marginal for towing my trailer in hilly terrain.
Gas engines, particularly big block gas engines, can do a creditable job of towing, but indications are that diesels pull better and last longer. Properly maintained and within its rated capabilites, you should not have problems with any of the major brand diesels. Of course, given the same environment, you shouldn't see any gas engine failure either...
If you provide the vehicle, what would they charge to convert it to RH drive?