Generic wifi adapters will not work with Xbox since you cannot install specific drivers on xbox.
Consider a powerline solution which will allow you to run an ethernet cable over your home's electrical wiring.
I can't as my broadband is down stairs and my daughters xbox is up stairs. I thought of tryin to hook up my old talk talk router some joe but I have t a clue.
You can find them by searching "powerline kit" or "homeplug kit" on Amazon, Google shopping and other sites. I suggest sorting results by highest rating/reviews.
By searching for "kit" you will make sure you get both needed pieces.