Hello Red.dwarf4ever,
As far as the plan, you'd want to check directly with your wireless carrier. When you add the mobile hotspot option to a cellular plan, most carriers have a separate data bucket for it. So while your cell phone plan might have unlimited data, the mobile hotspot service attached to your plan may only have something like 2GB, 5GB, etc. of data usage. Your wireless carrier will be able to confirm what data allotments their mobile hotspot plans offer.
If you're in an area where the iPhone only gets a 3G connection, the connection speed should be sufficient enough to perform most basic things, however if you're streaming something that is of a higher quality like HD or 4K, you may experience some buffering. It really all depends on the speeds of that 3G network. If you were to use the phone in an area where it's getting an LTE connection, the speeds will obviously be much better and there shouldn't be any issues with higher quality items.
Unless your computer is incredibly old, you shouldn't need any type of adapter to get Wi-Fi on it. Wi-Fi started emerging as an option in the early 2000's. If your computer was manufactured sometime within the last 15 years, it's pretty much guaranteed to have a built in Wi-Fi radio. If you're not sure, you'd want to refer to your user manual.
If the computer does in fact have Wi-Fi, then you would connect to the mobile hotspot just like any normal Wi-Fi network. On the phone go to Settings > Personal Hotspot, and turn on the "Allow Others to Join" option to enable the hotspot. Then on the computer just go to the Wi-Fi settings and connect to the network. The network name will be whatever the iPhone name is (Settings > General > About > Name).
How to set up a Personal Hotspot on your iPhone or iPad
Cheers!