The 52 and 58 are the diameter in MM of the front threads of the lens.
You can get a 58mm UV filter or a 52mm or whatever size you need for the lens in question.
You don't need an adapter unless you have a say a 52mm lens and want to use a 58mm filter so you get a step up adapter and step down if you are doing the opposite.
Generally you don't want to put a smaller filter on the lens you can go bigger but smaller and you start have issues.
k im a little confused here...sorry im new at this

my main thing for getting a uv filter is to protect the lens more than anything
so, in order to get one, i have to have an adapter, correct?
in this case, which is better for me to get 52mm or 58mm?