Baby quail need really high protein, 28 to 30%, for the first few weeks. Chick starter won't work, but some people use turkey starter successfully.
Once the birds get older and start laying eggs you can switch to 20% protein chicken layer feed if you supplement it a bit with other protein sources. Mine really like fish in the form of that fake-crab stuff and mealworms. Some people give them eggs, but I keep them for eggs, so that seems counter-productive. Other people give cat food.
For finishing meat birds, you should either keep them on 28% gamebird starter or put them on 24% gamebird grower. I suppose you could keep egg-layers on 28% or 24% gamebird if you heavily supplemented it with calcium.