Renting a car will not be such a big problem i expect every mayor airport for instance has car rental company's.
As for camping, I would recommend that you get lists of all campings in Ireland before you decide to go somewhere. I went there in 1998 and for some reason (the weather maybe), found that the Irish did not seem to enjoy camping as much as I expected.
There seems to be far less camp sites than in Scotland for instance (or at least we had more trouble finding some).
where abouts in Ireland do you plan to go ? I could recommend the West of Ireland, especially around, Galway and Clare.
If you're in Ireland at the beginning of July you will find a lot of people camping at Spanish point in Clare for the Willie Clancy festival. This is a traditional music week were you will meet people from all walks of life having a great time.
The weather can put a dampner on camping but if thats what you're into you'll have a good time anyway.
If you let me know when you plan on coming over and to which parts of the Island I can look into the best campsites etc and get you a list.
Renting a car should be no problem, there are plenty of companies to be found here to cater for most budgets, if you need any help or names of companies let me know...