There's no reason to carry a grease gun for wheel bearings. Even at the higher mileages, once a year greasing/repacking is plenty.
The other this is, many TT's have grease "systems" if you will, that allow you to basically flush the old grease out and replace with new. No repacking needed.
Check into what you have exactly on your TT before you go too much further.
The bearing buddies can get people in trouble. As mentioned, its more likely to blow out seals (which could easily go unnoticed) and contaminate brakes. They do come in handy on boat trailers, where they can keep a low, steady pressure of grease in the hub to keep water out at all times. Still, I would not say they are "needed".
As far as what type of gun to buy...well that's just personal preference.