First off, if you haven't made a cheesecake before, buy a springform pan. Better yet, get two.
I almost always make two cakes for parties, church, friends..and it's fun to experiment adding things to the basic recipe (more on that below!) :) Springform pans these days usually are available non-stick. WAY better than anything else.
When we get to ingredients and instructions, I'm going to give directions for a single cheesecake.
Second, I'm a pretty traditional baker so far as the "crust".
I know there are people who use pre-made dough pie crusts, pre-made graham cracker crusts (frozen) and simply pour the batter into these and bake. It's kind of like you get what you, um, ask for. Those types of crusts usually are mushy and don't really add much to the experience when you take your first bite of the finished product. There is nothing better than a smooth, creamy, delicious cheesecake surrounded by a crispy graham cracker crust! I recommend you get graham cracker crumbs (in a box, in the bakery section) and follow the directions (usually as follows):
Third, the cake.
Here are the ingredients for a basic cake (always appropriate without any additions, always yummy!):
Fourth, things that are nice additions to this recipe!
Here are a few things I have added:
Ghirardelli bittersweet chocolate, melted in a small saucepan, then swirled into the batter:
If you want to really be chocolaty, sprinkle bittersweet chocolate chips on top of the cake when you slide it into the oven. Oh yeah.
Berries (I really prefer fresh berries, but you can use frozen berries as long as they're first defrosted). Raspberries, blueberries, strawberries, blackberries.
Combining raspberries with chocolate is awesome!
Grand Marnier (if you like, you can simply use orange flavoring)
Kahlua (also excellent with chocolate)
Coffee (brewed strong, like a small espresso, so it doesn't make the batter too runny)
If you add things, especially cold items like berries, allow a little extra baking time.
Fifth, Serving your creation:
The cool thing about a springform pan is that with the flip of a latch the sides of the pan separate from your cake and you're ready to cut. I recommend you make cuts all the way across the cake, carefully going down into the crispy crust, and that you make each slice you want to serve no greater than an inch wide at the side of the cake.
Many folks will want smaller pieces, as this cheesecake is really rich, but if you cut sections on the small side and they're still hungry--or if you've made two or more varieties of cheesecakes, they can have seconds! It really helps to have a proper cake or pie server, and helps even more to have some hot coffee or tea to go with your cake!