More About offers and invitations

Would you like…? is the most usual polite question form for offers and invitations, especially in British English:

Would you like a cup of coffee?

Do you want…? is less formal and more direct. It is more common in North American English than in British English:

We’re going to a club tonight. Do you want to come with us?

Would you care…? is very formal and now sounds old-fashioned.