Equipment needs are pretty minimal. If you get a press, good quality cheese cloth and an accurate thermometer, you should be able to find all the additional equipment you need in your kitchen. You might want to consider a second, larger stock pot that your 1st pot will fit inside of. That way you can add heat to your cheese double boiler style and minimize the risk of scorching your milk. The site Selfors posted has some good step-by-step photo essays that should really help clear things up for you.
I'm glad you decided to do the more complicated cheeses "sooner or later" rather than jump right in to making hard or ripened cheese right away. That'd be a lot like jumping into all-grain on your first batch of beer. It isn't impossible but it definitly makes things harder. Trying a couple 1 gallon batches of cottage or mozzarella cheese to get a feel for how your ingredients act is a good idea.
A couple of unsolicited tips from my experience; 1-If using store bought homogenized milk, do NOT skip the calcium chloride. If you do, you'll get curds but they won't set as hard or quickly and the curds are harder to handle w/out falling apart in a pasty mess. 2-Using a gallon of 2% milk and adding a quart of heavy cream to it will make a smoother, creamier cheese than using a gallon of whole milk. I've found that a quart of heavy cream added to a gallon of whole milk is too much though. I ended up with a fatty, greasy cheese that wasn't very appealing.
I'd rather be a bad example than a horrible warning.