There are Instructables up on fresh mozzerella and ricotta.
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I find a Feta cheese is easy as pie! Check out my instructions here:http://goatcommune.blogspot.com/2010/06/making-cheese.html Mind you, this does require goat's milk, but I'm willing to bet that you could do the same with cow's milk with only a minor change in flavor.
What kind of cheese? Hard, soft, specific flavor or texture?
I'm a big fan of milder cheeses, like a mild provolone or swiss. Brie would also be a good option.
The easiest cheese to make for a beginner is goat cheese from yogurt. You need two things. Goat's milk yogurt and cheesecloth. When I made it I actually used a very tightly woven cotton dishcloth. Simply put the yogurt into the cloth, twist it up tight and secure it with twisty ties, and hang it over a large deep glass bowl using chopsticks. Put the whole thing into the refrigerator. The liquids will drain out of the yogurt into the bowl. You can help it along initially by twisting the cloth tighter to force liquid out. At some point you'll get towards the consistency of goat cheese. Here's a page describing it: http://www.redwoodhill.com/recipes/yogurt_cheese.htm