If you're in a cafe, would you say "I want a coffee or I would like a coffee" ?
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I suppose it depends who you hang out with.
Some people may even say "Give me a medium coffee." I'd find that appalling.
I'd like a cup of coffee, please.
I'd like a cup of coffee.
I'll have a cup of coffee.
I'll have (a) coffee.
Just coffee. / Just a coffee. / Coffee.
Not I want.