Congrats on the new rig!!!!
Definitely go with a 2500/250 since you are looking for a nice, used truck. Finding a F150 with the max tow and hd payload option or GM 1500 with the max tow package could be very tough!!!
BUT..... Don't rule out a 3500/350 srw either!!! About the same price as a 2500/250, but more payload for extra firewood or a larger trailer in a few years!!!
As mentioned, it can't be stressed enough it is all about the payload if the truck when towing... Passengers, dog(s), cargo in the truck, the hitch system, and the trailer tongue weight all are included in the trucks payload..... Weight adds up quick!!! The 1500/150's all have plenty of power, just not enough suspension once you start loading up with a growing family (kids only get bigger and weigh more), toys, bikes, firewood, etc....
Good luck!!!