I doubt they offer barbacoa bowls in the same sense that you're thinking. In fact, I rarely see the term "barbacoa," which refers to the method of cooking (baked underground). Most Barbacoa style meats are either "asado" (usually beef, or "barbacoa de res") or "birria" (beef or goat). Cochinita is the closest you'll find to what "Mexican" places call "pork barbacoa," which is really just pulled pork with a sauce (I highly doubt they cook it in a barbacoa). But try out asado and birria, you'll probably like them, and they're much more common than cochinita.

A good Mexican place will have a variety of meats, not just "chicken, pork, or beef," but variations on each. They usually give a simple set of options for their salads, but you can probably pick any of their taco meats (suadero, carnitas, al pastor, etc) to have with it if you want.

If your primary concern is calories, get corn tortillas, which are whole grain, have fewer calories than flour, and are are high in fiber (so they'll help you feel full on less). A good Mexican place will make their own tortillas or get them fresh from a local tortilliera, so they'll be way better than the crap at the store.