Definitely get a car - there are fun places to explore around there, like Kings Canyon and the Olgas (both IMHO more atmospheric places than Uluru itself, which is fascinating but a little overrun with tourists) which you want to explore at your own pace. The roads are fine - long, straight and empty - just beware driving at dusk or at night, as kangaroos are not very traffic-savvy.

lalala is absolutely right that no accommodation at Uluru is good value - I would either go for the top end (Sails) or the bottom end (the camping ground) but nothing in between.

Above all, have fun - it's an amazing part of the world!