You need to look at some travel trailers, different sizes, figure out how much space you need to live in. I'm alone, 29-foot motorhome has plenty of space for me, that is equivalent in floor space to 24-26 foot travel trailer. It was plenty big enough for two of us and could accommodate 6 people easily for a few days. A guy and his dog, even easier than two people, dogs don't get into that "I need my own space" mood that gets in the way of two people in a small space.
I'm expecting you won't be looking at anything over 28 feet, that's where the floor plans start making accommodations for even more people, such as bunkhouses for the kids. Even with the heaviest conventional construction a TT this size is well within the capacity of your tow vehicle.
Shopping new, I'd be looking at conventional construction from Northwood (Nash and Arctic Fox brands) or molded plastic trailers from Bigfoot or Oliver, but those are beyond your budget. Reason, however, is construction for four-season or at least three-season use.
You'll more likely be shopping used, then condition matters more than brand, you'll just want to stay away from lightweight construction (which gets there by thinner walls, ceilings, floors, lighter materials to build furnishings, lighter frames,,etc).
Biggest issue for what you want to do, where you want to do it, is finding a place that you can do it. You'll likely need full hookups, winter-proof water supply, and if staying through the cold seasons, a large propane tank with delivery service. Also, not always easy to find a place open year round and letting you stay indefinitely, as housing codes in developed areas often try to separate recreational housing (short term) from manufactured housing communities (we used to call them trailer parks) . Most places I've been in the middle of the country I've been able to find RV parks with long term stays (a lot of temporary work projects run a few months to several years), but noted on the news today a local RV park that had evolved to trailer park was shut down by county health and everybody thrown out.