Look at the weight ratings for your particular "as optioned" truck and that dictates what weight trailer you can legally tow.
The other way to do it is choose your trailer and then buy a truck that is rated to tow it.
Since you're looking at a 2002, I'll guess you're like me and.......ahem.......slightly cash flow limited.
A 2002 properly equipped 8.1 will be able to tow a fairly large trailer. A quick google shows a 10,800 lb tow rating for a 2002 2500 GMC, but that all depends on things like axle ratio, tow package, etc.
The max weight I could find for a 2002 2wd 2500 gmc was that 10,800 (http://www.edmunds.com/gmc/sierra-2500/2002/
). That is a good 1,000 lbs under your expected dry trailer weight of 11,800...then throw your stuff in there and you can add at least 500-1000 lbs more.
Check the option codes on your 2002 very closely when you look at it. The 10,800 was the max rating. If the truck you're looking has different options (IE: gearing, tow package, etc) then it's going to be rated less than 10,800. That 10,800 also might be with the Duramax, a gas truck may be less.
Like I said, check the option codes on the particular truck you're looking at....
Also, don't expect mileage anything like the tundra gets. Get ready to pay at the pumps for all that displacement.
With a ten year old truck and expecting to tow heavy with it (no such thing as a "light" 5th wheel), make sure you look it over good. Ie: inspection, pay a mechanic, service records, oil change records, etc.....