Two or three years ago I started making cheese. I started out with chevre, of course, and it has been a big success with people.
You need a good thermometer, that's accurate and easy to use. I started out with a Polder probe thermometer. These have a digital read out and a cable, and a probe. They're made for meat in the oven, but work really well for cheesemaking. The weak point of these is the probe, they quit after awhile, sometimes fast. I've tried three kinds now, and I wrap the connection of the cable and probe with that white stretchy plumbers tape. I think this helps the probe last longer, but they still are the weak point. (If you're going to use the probe in a roast, be sure to take that tape off first). You also need a way to hang the cheese, I have a chain hanging from my ceiling over the sink.
I think most of the other equipment you need to make chevre can be found in most kitchens. Or you can substitute something.
You need a good 8 quart pot, stainless steel or enameled. Aluminum will not work.
Making chevre is really easy. You heat the milk up to 86 degrees, I do this on the stove, stirring constantly. Add the starter and a bit of rennet, stir it in. Let it sit overnight in the covered pot, and in the morning you have a curd. It needs to be over 70 degrees F, in the winter I put it in my oven with the oven light on. That's all it needs to be warm enough.
You scoop off thin pieces of the curd with a slotted spoon, into a cheesecloth lined colander, and then hang the cheesecloth over the sink. Or you can put it in molds to drain. Let it drain 6-10 hours and you have chevre.
You need to make sure all the equipment that will touch the milk/cheese is sterilized. I boil water in a big pot and put everything in it. I also boil water in the pot I am going to warm the milk in, since I am not pasteurizing it. If you want to get a permit to sell chevre it has to be made from pasteurized milk, no matter where you are in the US, it's a federal requirement. If you don't usually pasteurize the milk you use at home and want the cheese for home use, I have had no issues with making it from raw milk. It keeps about a month, which is quite a bit longer than people say it will. My milk keeps at least two weeks, I never keep it longer than that, so I don't know how long it actually keeps. I don't intend to ever sell cheese, or milk either, so I don't generally pasteurize any milk.
How long it keeps and to some degree how it tastes depends on how the milk is handled. Other things can affect the flavor, such as the individual goat, and perhaps also the breed of goat, and maybe the diet of the goat. If the milk tastes different the cheese will too. I have not noticed any difference in flavor or texture between pasteurized and raw milk. Lots of people, especially Americans, are terrified of "goatiness". My chevre is not goaty at all. In France "goatiness" is desired. I think you have to cultivate a taste for it if it isn't common in your culture. But "goatiness" is a feature, not a defect.
You can flavor it any way you want, I like to add red chili powder, granulated garlic, and a bit of cumin and salt, in between layers. Fresh basil leaves are good too, but fresh herbs limit the amount of time the cheese will keep to less than a week.
Chevre is very easy to make and hard to mess up. If you are just starting I recommend getting the chevre starter packets from New England Cheesemaking supply http://www.cheesemaking.com/. They contain a mesophilic starter and the right amount of rennet for a gallon of milk. After you have it down you can move on from there. I hear you can use buttermilk for a starter, but if you do you need to add rennet. The "rennet" in the grocery store isn't the right stuff.
Next I will talk about my Camembert adventure.
Have a wonderful day!