Could you / Would you + [verb] …?
Could I + [verb] …?
Would you like + [noun] / to + [verb]?
Would you mind + [verb-ing]?
Could you + verb asks someone to do something. It is more polite than can you.
Would you + verb is just as polite.
Could I + verb asks for something for yourself, or asks if you can do something.
Would you like offers something. After it comes a noun, or to + verb.
The answer is often Yes, please or No, thank you. For what you want, say I'd like: I'd like a coffee, please.
Would you mind + verb-ing (waiting, closing) is a very polite request. It means "Is it a problem for you?", so No, not at all means yes, you will do it.
Can you…? is fine with friends and family. Could you…? and Would you…? are better with people you don't know, in shops and at work. Adding please makes any of them softer.