B^2
Observer
Is this still your primary use case? If so what size travel trailer are you considering? Something modest that can sleep a family of 4 and a dog, has a bathroom, and kitchen could weigh as little as 3500lbs on a single axle. You could also want to tow the taj mahal. More realistically for a bumper pulled travel trailer upper limits are probably around 34 feet in length and somewhere just north for 10k lb gvwr.
On paper a half ton can tow any of the above, in practice a half ton is probably best up to about 5000lbs and mid 20s for length. If payload in the bed is of concern combine with the tongue weight a small travel trailer around 4000lbs should still be no problem.
If plans include a trailer over 5000lbs and a loaded down truck it'll still be do able in a half ton but will be more comfortable in a larger truck.
For Lariat trims I'd expect about 1600lbs pay load in an F150 with the 3.5 ecoboost and roughly 2900lbs give or take for the F250 with the 7.3. Bumping to an F350 with the 7.3 pushes 4000lbs for comparison sake.
The information provided in this post does not, and is not intended to, constitute legal advice, instead, all information, content, and materials available in this post are for general information purposes only. I am not a doctor nor have I ever claimed to be a wise man
As far as a travel trailer I'd probably be looking at the Micro Minnie 2100BH from Winnebago or maybe the 2301 BHS but that seems real big. We've got a 2nd kid coming in the early fall so not sure how much adventuring I'll be doing but it's definitely something I think about.