"I want coffee. I do not want milk."
I take chinese at my school and 想 is a better way to say want than 要。要means like must have
This is correct, but not correct enough. 我想咖啡 would be like "I think coffee".
想, when used alone, is almost always intransitive. With only two exceptions:
The object is a person (or more), where 想 means miss: 我想你 = I miss you.
The object is the word thing, or other similar abstract idea, where it means think and has the same usage as "think" in English: 我在想为什么他没有来 = I'm thinking why he didn't come.
When 想 is followed by a verb, it means want to + verb.
我要咖啡 = I ask for coffee. 我想要咖啡 = I want to ask for coffee. A more polite expression.