If you are planning to take just portrait photos at the start you have many options. Doing event photography such as sports or performance (bands, dances...ect.) you would need a camera with a fast burst mode (continuous shooting). That is what some of the cost of the more expensive cameras is for.
Some good cameras to look at as portrait cameras are:
Sony a300
Canon Xs
Nikon D60
As for the printer...if you are going to print just 4x6 prints (which I would suggest) look at the Epson
Picture Mate found here:
http://www.bestbuy.com/site/olspage...It has a built in card reader and screen so you don't have to use your camera as a pictbridge.
Printing a 4x6 on the spot is great and if your customers want bigger prints they can order them and you can print them out at home later. People at parties don't usually plan on carrying a 8x10 photo around with them.