I'd get the 15K A/C. There have been a few times it would have been appreciated. 13.5K cooling our 30' unit in 105ºF heat is really tough. I don't think it cycled off for a week!
Depending on the hitch your getting that price could he high – check around. Learning to set up your hitch is a VERY valuable lesson. (To me at least.)
I suspect your Tundra will tow fine, but you MAY be close to or over your GVWR on the Tundra. I'd say only a trip to the scale with a loaded rig will tell. You say the TT is under 6k dry so not too heavy.
Your gonna love it. Have fun out there.
