Depends on what species of bullheads, some only get up to 10" while others get up to 18". Since OP is living in New Jersey, there should be two bullhead species, the brown bullhead and the black bullhead. Both species get quite large, often passed 12". IMO a 125gal is prefect tank to house a mature bullhead, but a 50-75gal should be good growouts for young bullheads, they grows big quite quickly in first year.
As for foods....anything you can feed to them. I owned bullheads in the past and they eat everything from tropical fish flakes, betta food, triop food, shrimp pellets, live foods, frozen bloodworms, dried krill, goldfish pellets and goldfish flakes...pretty much everything.