We love our Suburban. However, if you don't need more than 4 people inside, I recommend a pickup. They are cheaper, generally have more available payload, and far more plentiful both new and used. They also have great storage for all the dirty stuff people take camping with them. A $150-2000 bed cover makes for the world largest trunk.
If you insist on the Suburbans, I highly recommend a 3/4 ton. The 2000-2006 come with either 6.0L or 8.1L. The 6.0L offers more capability and similar fuel consumption so the 5.3L in the half tons of same generation. The 8.1L is nearly unmatched for towing power, at the cost of lots of fuel. That's great if dedicated tow vehicle and was my first choice before buying new in 2011.
Before committing any tow vehicle, take a look at the TTs you want. Anything over about 6000 pounds dry will be better suited to a 3/4 ton. But TTs get crowed in the 5000-7000 pound dry range. You'll have to take a look and your own compromises.