A good vacuum with a good beater bar, to be honest. I went out and bought a canister (better than upright) with the biggest motor I could get and it works great. I never sweep, you're right it just flies everywhere. plus I have hardwood floors so sweeping isn't a good idea for them.

ADDED:
It's the upright, trust me. A canister really does work better in case you've never had one. Plus the size motor on it is a big factor. With all the animals I have I know how you feel, but hair stuck in the carpet isn't a problem here anymore. For a better food, that's smart thinking on your part. I'd suggest looking at this web site and search for something in the 5 and 6 star range GL

http://www.dogfoodanalysis.com/