In this post, I'll quote Baruch Levine's discussion of the rationale behind Leviticus 11's food laws. It's on pages 247-248 of his Jewish Publication Society commentary on Leviticus.
"The dietary laws of the Torah institutionalize the basic distinction between pure and impure living creatures. A practical system of food selection emerges, in which several factors interact. (1) There is a clear preference for domesticated land animals and birds, and the perception may carry over to fish. (2) Within this larger framework, concern is shown for the diet and digestive processes of living creatures, as if to ensure that nothing forbidden to the Israelites as food had been eaten by the living creatures themselves. If there was, there was concern that such food had been digested as thoroughly as possible or, at the very least, could be separated from the creature after slaughter. The permitted animals are herbivorous ruminants, whereas virtually all forbidden birds are carnivorous creatures of prey. The torn flesh of a land animal (terefah), the evidence of violent preying, is strictly forbidden, just as humans may not eat flesh that they have torn from a living creature. (3) Empirical evidence shows a correlation between methods of locomotion and patterns of feeding and digestion: In most cases, herbivorous ruminants have a cleft hoof. On this basis, creatures with truly cleft hoofs, two 'toes,' were considered domesticated, thus permitted; living creatures with paws were undoubtedly regarded as bestial and, hence, forbidden. (4) As regards fish, the biblical inventory is extremely limited. Preference for undulatory locomotion with fins probably correlated with observable feeding behavior. Crustaceans, for example, were perceived as scavengers."
So here are the criteria, and I draw some of this from Levine's actual comments on the text of Leviticus 11 (specifically page 66):
1. God doesn't want the Israelites to eat predators or scavengers. One reason is that eating predators could result in the Israelites consuming an animal who has eating something that is prohibited to the Israelites---such as an animal that was torn.
2. God also doesn't want the Israelites to eat anything with paws---which is bestial. That's why the command is that they eat creatures with cloven hooves---any other type of foot constitutes a paw. God's preference is for fully domesticated land-animals. But I'm unclear on this point, because Deuteronomy 12:15, 22 and 14:5 let Israelites eat the gazelle and the deer, which are in the wild.
3. God wants the Israelites to eat animals that chew the cud, meaning they thoroughly grind and digest their food. That way, if the animal does eat something that's forbidden to the Israelites, his bodily processes would dispose of it (I guess).