The type of truck you get will depend on the trailer you get. For 50k, unless you're buying used, won't get you a big monster triple axle or anything like that. I'm going to guess, just based on price range, that you'll be fine with a 1 ton SRW diesel.
The next suggestion I'll make is to just look through plans online, at RV shows, etc., to decide what kind of floor plan you like. Think about whether it will fit your needs for full time living, have the right storage, and the right features for the kind of traveling you'll be doing, for example, if you're going to move around a lot, you'll probably want auto-leveling. But if you plan on staying for longer periods of time at each spot, auto-leveling is probably not that big of a deal. Also determine what size garage you need. I know for us, we wanted to be under 40', double axle, with at least a 12'6" fully enclosed garage. So our choices were very limited, and it ended up coming down to just choosing which manufacturer. Every trailer with our requirements had the same basic floor plan.
2020 Keystone Montana High Country 294RL
2017 Ford F350 DRW King Ranch
2021 Ford F350 SRW Lariat Tremor