There are a lot of interpretations of "mexican" cuisine in the u.s. For example, in California, burritos and tacos are seen as the pinnacle of mexican food, but from what i understand burritos (at least the way we make them) are not too common in mexico. Burritos are usually made with flour tortillas and are filled with rice, beans (usually pinto, black, or refried), and a variety of meats--carne asada (roasted meat), chicken, beef, or carnitas (a yummy pork concoction), and sometimes shredded cheese (cheddar, monterey jack, or mozzarella work well), sour cream, and guacamole (mashed avocadoes with lime juice, hot peppers, garlic, onion, and sometimes tomato). Tacos are usually made with smaller corn tortillas (and yes, you should heat them up so they get soft enough to bend without cracking), and feature many of the above fillings minus the rice and beans, which tend to be on the side.
A fabulous book on the diverse cuisines of mexico is diana kennedy's cuisines of mexico. http://www.amazon.com/gp/product/0060915617/sr=8-5/qid=1147398146/ref=pd_bbs_5/103-1740631-3961412?%5Fencoding=UTF8
. Kennedy's book shows that the different regions of mexico have wildly diverse flavors.
Some ingredients that you will likely need to cook mexican food: cilantro, avocado, limes, garlic, onions, beans, corn, hot peppers (such as jalapenos, habaneros and chipotles), hominy, various meats, for coastal cuisine you will likely need fish, scallops, or shrimp.
Sorry I don't have recipes exactly, but i hope this gets your imagination going at least!
Oh, and refried beans are traditionally cooked with lard.
Ya I don't really agree with the California thing I tinhk if you live close enough to the border you get a pretty good taste of what real mexican food tastes like.I live in the San Diego area and there are lots of real mexican food places that serve food just like what you mentioned before!