How high you need the car depends a little bit on the type/length of the headers from what I hear, but I'm pretty sure you can get the car high enough with just jack stands or barely high enough. Personally I would get a couple more jack stands and you may need ramps in order to get all four tires off the ground because of the lifting points. I've never lifted all four tires off the ground with out ramps.
Do a search in the C5 forums on "header installation" and you will find detailed write-ups on the process. I would also suggest having a buddy help as it will make the install easier.
Here's a sample of many install dyi's
http://97vette.com/howto/headers/index.html