How many people in the truck is a factor but I'm guessing not too many and not too big with that size trailer.
I'd be surprised to see anything other than 3.73 gears in that truck. And I'm presuming it's a 5.7/350. The Vortec 350 likes to rev, but not as much as the LS engines. Starts building good power around 2500 up to 3500 or so, show is pretty much over by 4500. Your generation truck does not have Tow/Haul so be sure to use 3rd gear manually. Fresh transmission fluid is essential to keep the 4L60 alive. Use regular plain old Dex/Merc, no Synthetic and especially no Dex 6 in there. Add a pint of Lube Gard Platinum to the Trans too.
One challenge with the Suburbans is they tend to be a bit saggy in the ass end as they age. Also, the trailer ball is about five feet from the rear axle which is a bunch of leverage. A Weight Distributing Hitch is a must, and a set of airbags will make your towing experience much better too.