I voted rats because I feel they're more valuable and make a more complete diet.
However some balls are picky and will only take either mice (I know of breeder females who eat exclusively mice and they're just fine, popping out great clutches and all) or just ASF's, in which case that would obviously be the better prey item. Either way, all three are good food sources in my opinion.
I wouldn't go for bird, and as stated gerbils are addictive and expensive, and hamsters are pretty pricey too.