Your limiting factor is going to be your budget on this purchase. You are getting some advice of what would be more ideal, but I think you might need to look at what is workable.
I just went through a search for a Suburban. I narrowed my list to a 2500 with the 8.1, and found that those are few and far between. Unless you are looking at vehicles above 250,000 miles, a 2500 burb will be out of your price range.
The Ford V10 Excursion would be a better tow vehicle, and I was able to find a few of those in decent condition that were in your price range. You might look that way.
As far as 1500 Suburban's, they are rated to tow that weight. It might be slower than you would like, but if it fits your budet you might have to make some compromises.
If you go Suburban, take a look at the hitch. Unless it is aftermarket, it will likely be rated to tow 5000 pounds. It is worth looking at changing out to something heavier duty.
Good luck with your search.
