Wireless display/Miracast in general isn't ideal for something interactive because there's usually noticeable input lag. It's mostly used for consuming media. As for Ubuntu Touch, the compatibility is a bit hit and miss so it's hard to tell if it'll work on your monitor or adapter. It may also depend if the port works well with wireless display. Known adapters that works "well" are the Microsoft ones. I personally wouldn't recommend buying a monitor just for this. I don't even know if there are monitors that has built-in feature like this unless they have features like a TV. You can look for adapters however. In any case, do not expect a good experience with it especially thinking you can use it like a desktop.