When I hear back country I'm assuming back packing, so that's what I'm going to start with.
You need shelter, a cook kit, a sleeping system and something to carry it all in.
Shelter can be a lot of things depending on where you are going and what season it is. In the rockies in the middle of summer a tarp and a ground cloth is all I would need. Push that till September and I want a tent with full rain fly and a vestibule. If you are an A&M student you can rent decent back packing tents from TAMU outdoor program. Keep in mind backpacking tents are small, there is just room in there for sleeping and if you are with someone your sleeping bags are probably touching.
Cook kits are pretty simple, a pot and a burner. This Stanley pot from Walmart,
https://www.walmart.com/ip/Stanley-Adventure-Camp-Cook-Set-Stainless-Steel/16784406, works fine and will last forever. Dump one of the cups and add a small fuel canister and this burner,
https://www.amazon.com/Titanium-Backpacking-Miniature-Ultra-light-Camping/dp/B01N5WRJ8A/ref=sr_1_10?crid=1VVNBTTOWMNXA&dchild=1&keywords=ultralight+burner&qid=1597162958&sprefix=ultra+light+burn%2Caps%2C170&sr=8-10, and all you need is a spoon to eat with.
With the sleep system, again it depends on when and where you are going. You want to start with a pad, you need something insulating you from the ground. You can get decent foam pads for pretty cheap and they always work and won't ever deflate in the night. Next is the bag, if you are going to spend some money this is where I would suggest doing it. In general the temp ratings are for lower limit or survival ratings not normal comfort level. Some higher end brands will show both of these numbers, but as a rule of thumb I add 10 degrees from the number on the bag and use that as my lower limit of comfort, a 30 degree rated bag would be comfortable at 40 degrees. Some colder sleepers, my wife for instance, want more like 20 degrees to stay comfortable. Temp ratings are also tested for a person in full base layer clothing with socks on. These can also be rented from TAMU Outdoors.
If you think you are going to do this more than once then backpack is the other place I would suggest spending your money. If you are going to cover very many miles at all, having a pack that fits you well and has a good weight belt system is critical. For $200 this is a really good pack from REI,
https://www.rei.com/product/148589/rei-co-op-flash-55-pack-mens?cm_mmc=aff_AL-_-34947-_-46631-_-NA&avad=46631_d1c511155&CA_6C15C=120217890006153853, but you need to have it fit and set up for you. There are sizing instructions online and it's not to hard to have a friend measure your torso length.
TLDR: you can rent most from TAMU Outdoors, get a good pack and sleeping system with a pad.
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