We have a 2011 Armada and have towed a 25' TT (5,300# empty / 7,300# loaded) with it for the past four years.
Lots of folks in some of the parks we pass through while traveling are living there full-time and working in the area, so your basic idea is sound.
For the last two summers we've done more extended periods of camping, spending 2-3 months at a time in the trailer.
First thing: RV'ing is fun while you're on vacation. But when you're using a trailer as a full-time residence, it's just a place to live and nothing is as convenient as living in a house or an apartment. So you're going to be making compromises and will have to accept that from the outset.
Rent always costs something. You'll need full a full hook-up site (electric, water, and sewer). If you're there for more than a month, electric will probably be metered and will be in addition to the monthly site charge. How much you pay for your site is highly dependent upon the geographical area you are in and (if there short-term) the time of year. Tourist season will always be more expensive unless you're "permanent".
You'll probably be in commercial parks a lot more than state and federal parks, due to time limits in the state and federal ones, and the fact that sewer hook ups are less common there (not having a sewer hook-up gets old really fast).
You really need to do some research into park costs in the various locations where you might be staying. Here in Florida all the parks fill up in the winter and if you want a reservation you have to book far ahead - as much as eleven months for some state parks "in season".
Where we stay in the summer - out in the boonies in the mountains of North Carolina - we currently pay $1,500 - $2,000 for the 6-month summer season + electric ($50 or so per month)... which is very cheap. But we aren't close to large cities, and due to the weather, most of the parks are closed for 6-months.
Next thing is the type of trailer. In our experience, very few people who live for in an RV for extended periods do so in a bumper pull trailer. Even for one person, the lack of room - especially storage room - becomes a major issue. Most longer-term folks have a 5th wheel. It doesn't have to be a huge 5th wheel, but 5th wheels have much more room, especially storage.
We use the Armada for storage, but even for only a few months it becomes an aggravation - especially when you need to make a haul at the grocery store. Even with the third seat stowed, there is little room back there for much else, unless you move stuff into the trailer temporarily... and that includes all the extra hanging clothes that are blocking the second seat.
Of course, you'll need a pickup truck for a 5th wheel, not an Armada. A small 5th wheel can be managed with a 1/2-ton (about the same capacity as the Armada), but most folks use a 3/4-ton for small 5th wheels.
Although you can get by with a 2-door truck, a 4-door is more practical. In order to retain the ability to park in "normal" parking spots at the grocery store, you need a short bed truck with a sliding hitch in the bed (in order to make tight turns without running into the front of the trailer with the cab of the truck).
There's always a trade-off: You can't put a fiberglass cap over the bed. But you can install a roll-up cover in order to use the bed for groceries and storage of less valuable "stuff".
Not trying to discourage you from the Armada/bumper pull TT, but you're wise to start this whole process early. It sounds like you'll be spending most of your time actually living in the trailer, rather than towing it around the country sightseeing.
Before you buy anything, I'd advise you to visit some local RV parks and get some advice from folks staying there. If you stop at the office and talk to the folks there, you can get an idea of the monthly costs and they'll probably let you drive through the park and talk to some of the residents who might be outside, although at an extended stay park most of them might be at work during the day.
Basically, you first need to research the type of lifestyle you're envisioning and then decide upon a particular vehicle and trailer accordingly.
Good luck