I think any of them are a good choice, the 5 speeds work just fine for towing they are the same gear ratio wise as the 6 speeds except for the additional overdrive gear. So the 6 speeds should get a little better empty highway economy but its not significant enough to be the deciding factor. The 5 speeds will not handle as much power though, their weak link is in 5th gear (mine would slip on a 70hp tune) and this becomes more pronounced with more miles. But if your planning on running more than 100rwhp over stock on either a built transmission will be required sooner or later.
Now for the motors, the LB7 (2001-2004.5) and LLY (2004.5-2006) have weaker rods than the newer motors, they are typically good for about 550rwhp. Where as the LBZ's (2006-2007.5) are good for almost 650hp. But the LB7's and LLY's have better pistons, the LBZ's are prone to cracking in half, not all that common but there seems to be little reason as it happens on stock and modified motors alike. The injectors on the LB7's had issues, they tended to crack and because they were internal would dilute the engine oil with diesel. There are very few LB7's that haven't had the injectors replaced at least once. The newer motors have better injectors but still can fail, but less commonly. The newer motors have more emissions equipment which can cause issues, but as for fuel economy they all seem to be similar (2001-2010) with the older motors tending to have slightly better economy.
As for EFILive, if you plan on doing the tuning yourself the LB7's are by far the easiest, as they don't have a VVT and there is far less tables to play with. But either way I would also recommend both boost and pyro gauges with any power level over stock while towing.
But as long as the truck is in good condition, has been well maintained, and is priced right I don't think you can go wrong.
By the way here is what I have.
2002 Chev CC/SB 4x4 2500HD LB7
S&B Intake, 5" MBRP, BD Wastegate Actuator, BD Trans Converter Flexplate, EFILive by Me, FASS Titanium 150gph, Autometer Pyro and Boost Gauges
I also dynoed 507 hp / 883 ft*lbs on my dyno only tune this summer.
Hope this helps.