Any of the books or websites mentioned above are great places to start to learn the techniques behind making cheese. I'll give my recommendations as to the order or cheese types to pursue when first starting out:
Yogurt or buttermilk: practices sanitation and culturing with starter bacteria
Strained/Greek yogurt: practice draining a lactic-set curd into a thicker product
Ricotta/Paneer: a first more solid type cheese, and quick to make
Fromage blanc/quark/chevre: made similar to yogurt, but uses some rennet, and is then drained in cloth for a soft fresh cheese
30-minute type (using citric acid powder) mozzarella: uses more rennet, involves cutting curd and separating from the whey, which is the basis for most all hard and aged cheeses. Is also then heated a stretched (unique to this family of cheese), and is quick to make and eat (thus rewarding!)
Next comes the wide world of aged cheeses. These all involve culturing milk (a bit) with starter bacteria, adding rennet, cutting the curd, and draining the whey. Most also involve heating or cooking the curd, then pressing into forms:
Feta: doesn't involve cooking the curd or pressing. The curd is drained in a colander or form, then brined in salt water for a few days up to many months.
Gouda or Edam: a simple first hard cheese, in my opinion. The curds are cooked by adding hot water to the pot rather than heating in a "vat." This is a washed curd technique, where some whey is removed before the hot water is added. Then the curd is drained from the whey and pressed in a mold with cheesecloth, but doesn't require too much pressure to get it well formed. Then is is usually brined, and can be aged for 6 to 8 weeks for a mild yet tasty cheese. Can be waxed or vacuum bagged, the easiest for first time aging.
Then it gets more varied which direction you could go. Can try more types of hard aged cheeses, like Jack, Caerphilly, Cheddar, etc. Caerphilly is a favorite here on the forums. Extra hard cheeses like Parmesan and Asiago, and cheeses with Large Eyes like "swiss," are either a bit more complicated or simply take a long time to age. But there's also the bloomy rind, blue-veined, and washed rind types to explore:
Bloomy rinds like Brie and Camembert: made, at first, similarly to feta, but involve the addition of special mold cultures. Care is taking during aging to maintain the right temp and humidity. But if all goes well, in 3-4 weeks they are ready.
Blue-veined: ugh, trickiest for me! Blue molds are more sensitive to the right acidity and salt levels, and also are rather particular about the aging environment to go well. Usually involves piercing the formed cheese with needles to allow air into the center for the mold to grow.
Washedirinds, like munster, brick, limburger, etc: also made similar to feta and brie at first, but then require frequent washing (yes, literally) of the rind with a damp cloth or hands with a mild brine solution with a special b. linens bacterial culture to develop orange-red "schmear" on the surface, for a pungent but soft-bodied cheese.