I think I'll just chip in a bit here.
The ideal solution for your application is to use an identical pair of printers connected to the PC and set up as a pooled pair. You can google how to "pool printers". It is simple, does not requirea additional software and is built into Windows. If I were doing this I would actually take along a pair of Epson printers with a CISS installed. With the given application, it is possible to output around 3 5x7 photos per minute with this setup and this would alleviate any kind of lineup or delay if something like a pair of Epson R260s are used. You can use a Canon but the issue of cartridge changeout will crop up and delay things and your workflow. In any case pooling two printers is highly recommended if you want a smooth flow. Otherwise you may face a bottleneck situation due to printing if there is haevy traffic at certain times. For these situations CISS equipped printers are ideal.
The other consideration is to use software such as that created by Breeze Systems. Their software has a photobooth mode, but you can set it to take single portrait shots rather than "fun" shots. This is even more so, since you can orient the screen to face the family thus allowing them to see themselves at the time the picture is taken.
http://www.breezesys.com/
With the appropriate models of cameras, their software is superb for your application. Expensive cameras are not necessary at all, but will depend on the quality you require. I will suggest that something as outdated as a Canon A70 or A60 which is totally a dinosaur in some consumers eyes and worth next to nothing will amaze you in this application. This is so because they are able to provide a live view and can be controlled by a PC. Thus there would be no requirement to remove memory cards to print. You take the picture with the camera connected to the PC and the picture will immediately start to print. This explains the suggestion for the pooled printers.
Ideally however, you will want to use a camera that communicates with USB2.0 to minimize the time required to get the picture into the pc from the camera. Unfortunately Canon has removed this tethered shooting from their current lower priced Powershots but it still remains within their better Powershots and superzooms. On the older Canon cameras even the 2 and 3 megapixel models had this feature. So a simple 2 megapixel point and shoot all the way up to a dSLR with umbrella flashes is possible.
Surprisingly, you will need a faster or a more current PC if you have a lot of traffic. While I appreciate it is 200 families within a day, do consider the peak periods as that will determine your hardware needs.
I have a setup that does exactly what you seek to do. It's wonderful.
