Your ricotta wasn't traditional stuff, which is made with the whey left over from making other cheeses. Ewe whey, specifically. When you make variations, you can just specify: goat, whole milk, etc. Whole milk ricotta (aka sweet ricotta) is made from whole milk and curdled with citric acid. Whey ricotta is curdled with vinegar and, optionally and flavorfully, bacterial cheese starter. You can actually make ricotta from just reheating the fresh whey without using an acidifying agent at all. There are many ricotta recipes that use skim, lowfat or whole cow milk with vinegar. They have a nice texture and much higher yield than traditional ricotta. I haven't run across too many nomenclature purists - just call the cheese what it is: "(Vinegar) whole milk ricotta," for the cheesmakers; "ricotta" works fine for the cheese-eaters.
You can have such fun with the soft cheeses! They're the ones to start with even if you want to work your way up to the hard stuff ;-)
You've got your lactic cheese, fromage blanc, chevres, mascarpone, buttermilk cheeses, yogurt cheese, kefir cheese, lemon cheese, panir, brousse, neufchatel, gervais, bondon, chream, ricotta salata (a great first-hard-cheese to make, easy and delicious), chenna, queso blanco, queso fresco... and then there's cottage...
Most of these can be used in any recipe wanting ricotta or cream cheese. Most of them can be made with nonfat or low fat milk with little or no loss of quality. Home made nonfat cream/soft cheeses are MUCH more like the full-fat store versions than the awful nonfat store versions.
There are two cheesemaking books I recommend: Home Cheese Making
If you do want to progress to other cheese types, ricotta salata might be your first, then most people try mozzarella first. If you want to be happy with it, use a cultured recipe.