> Like "I'll have 3 loaves please". I guess it would be like 三个 or similar?
That's it exactly, and it's very common. Any time the noun is clear from context, you can leave it out. (You shouldn't leave out the measure word though - where in English you might have "I'll take three", in Chinese you'd still want 三个.)
If you walk into a restaurant, someone will ask 几位 "how many?". 几 is a question word for small numbers, and 位 is a (formal, polite) measure word for people.
Also thanks for saying that they're equivalent to things like "Schools of fish" or "loaves of bread". They make way more sense to me now!