You have 2 basic options. You buy a intenal PCIE card or you use a USB device. In general the PCIE cards tend to be more powerful but you can get USB devices that work the same you just need to avoid those tiny devices.
Mostly this is going to be a personal preference.
With your budget you should have no issues getting a quality card. In both types of adapters you want a way to move it away from the metal case. The best PCIE cards come with short antenna leads that let you mount the antenna on the top. USB you can of course just use a USB extension cable on any but the better USB devices generally already have a base and extenstion cable. They also tend to have larger antenna. Again the USB devices to avoid are physically small devices that are designed where portability is more important than performance.
Since you do not control the router there is no reason to buy some really fancy wifi card. They landlord likely is cheap and runs pretty basic stuff so you running a fancy card say that supports wifi6 likely is a waste of money. I would stay with a fairly basic device that has 2 antenna. Most these devices will have a 1200 number on them.
You should be able to find many within your budget.
Actually there's a third option and it's the one I chose for the best possible bandwidth and signal strength.
I used an Asus router that has "Media Bridge Mode." This allowed me to use the 4x4 radio to connect to the main wifi of the home, and allowed 4 devices to connect via ethernet in my office room when I had an apartment. I thought this was the best option because the radio circuitry is top notch in a router compared to a USB adapter or PCIe adapter. Of course, the OP would need a spare router laying around at home to do this with. If not, then the option from Bill would be good.
I'll reiterate what he said, don't buy those tiny nano USB wifi dongles. They're great if your in the same room as the wifi router, but the range on those is terrible due to the lack of a real antenna.