How much space do minnows require?

I know that goldfish need a lot of space, an I am set on "rescuing" a few feeders. However, I don't want to get feeder goldfish as I know I cannot provide them with a sufficient tank. I was thinking about getting minnows, as I'm upgrading my betta tank to 10 gallons. Is this healthy, or are they great waste producers too? If not, how many can I keep?