Your stove will be your biggest limiting factor. IF you can get a full boil going with 6-8 gallons of wort, you're golden for a full AG setup (cooler mash tun, etc.). If not, then you could opt to go with electric kettles (if the electrical in the place will support them). If you have a place where they allow you to have a grill, then you could get a propane burner for the boil. Use the stove to heat the mash/sparge volumes and boil on the burner.
OR get a friend/family member to host your brew sessions (that has a house). That would solve those issues for you.
I'm in a similar position. My LL doesn't want (without increasing the rent
) brew/ferment here at home. SO, I brew/ferment at a buddy's place. I lucked out when that option presented itself. I simply lug my brew gear to his place and setup on the porch. He brews (BIAB) in the kitchen, while I go with the cooler mash tun out on the porch. We're typically done about the same time, or close enough. Plus, we get to talk about brewing with someone else while brewing. :rockin: The only down-side of this setup is that I'm restricted to brewing when his schedule allows. Luckily, that's about every two weeks (roughly).
If you can get into a similar situation, go for it. If you can store a good amount of your gear there, even better. I carry most of mine with me, simply to keep my options open for other brewing opportunities.
[edit] Since you can do gas (propane I assume) burner outside, that should solve the issues for you. Just get a 10 gallon cooler/MT and a kettle (or kettle and pot) for heating the mash and sparge volumes (you'll need something to catch the wort coming out of the MT). I originally used an 8 gallon aluminum kettle for the mash water heat and wort boil. I used a 5 gallon SS pot to heat up the sparge water. Get a good wort chiller and you're set.