The Mexican cheeses with which I am most familiar and use most often are Queso Fresco, Queso Blanco, Queso Añejo, Cotija, Oaxaca, Asadero and Panela. To be quite honest, many of these have the same texture and taste more or less the same.
Cotija, queso fresco, asadero, queso blanco and panela, to me are very similar and I use them interchangeably. Those who are true connoisseurs of these cheese would most likely disagree with me.
While they are slightly different cheeses, queso blanco and queso fresco 
are similar in taste and texture and the main difference is in the way they are made. Both are easily crumbled and do not melt. You can grill a piece of either cheese on a hot griddle, let it brown on both sides, making a delicious bite of warm cheese. Both cheeses are used to top off a tostada, corn on the cob, enchiladas, eggs, salads, beans, etc. The flavor is mild and even though it may have a slightly salty taste, both cheeses are low in sodium and fat. Both are made from raw cow’s milk or goat milk or a combination of the two. Try using either of these two cheeses in place of feta for a fresh summer watermelon salad. Queso blanco and queso fresco are both un-aged cheeses.
Queso Añejo is an aged queso fresco and is made from goat’s skim milk, but can also be made with cow’s skim milk. It is rolled in paprika (I have found it rolled in sweet, hot and smoked paprika). This is a popular cheese used by the purists for the filling of cheese enchiladas. 
Most Americans are used to cheddar or monterey jack cheese. Much like the Spanish Manchego cheese, the younger aged añejo is softest and it hardens the more it is aged. A well aged añejo has the texture of Parmesan cheese (making it easy to grate) but does not taste as strong. In its younger form you can crumble it on tacos, tostadas, corn, salads, etc.
Cotija cheese is a hard cheese made from cow’s milk. It was named after the town where it originated, Cotija, Michoacan. This is probably the saltiest of the Mexican cheeses and considered an artisan cheese, made by hand. It is produced only in the months of July through October. It is very close to feta cheese in texture and flavor, but I think it is a bit milder than feta. This cheese also does not melt. Like many of the others, it is good crumbled or grated over traditional Mexican favorites mentioned above. The saltiness of the cheese makes it a good contrast grated on top of fruit. It is also used in casseroles and some even grate it on pasta.
Oaxaca cheese is similar to queso asadero and Monterey jack cheese. It was first made in the state of Oaxaca, Mexico, thus its name. Queso asadero started in the northern state of Chihuahua. Oaxaca cheese is much like string cheese and the texture is like mozzarella cheese. 
The making of the cheese is a method brought from Italy where mozzarella is produced. The cheese is stretched in long ribbons and rolled into a ball. Asadero cheese is a mild semi-soft cheese that is also similar to string cheese and has much the same properties as the Oaxaca cheese. Both cheeses are great cheese for chili con queso, quesadillas, empanadas and chili rellenos. You can easily use them interchangeably.
Queso panela 
is a smooth white cheese made from pasteurized cow’s milk. This is an excellent cheese to serve on a charcuterie board for a party or appetizer. It has a mild flavor similar to mozzarella but has a softer, creamier texture. It can be served heated or as is, covered with a chutney, jam, or savory topping such as an olive tapenade or hot sauce. Panela is also similar to Paneer, an Indian cheese. It too, like many of the other Mexican cheeses can be crumbled over many of the foods mentioned above. I like it crumbled over my guacamole mostly for presentation.