As everyone has pointed out there are pros and cons to both. I think for your first trip, though, you should, if you can afford it, stay on site at a WDW hotel (I do not consider DD hotel or S/D truly onsite and have stayed in both). While there are lots of great offsite options (and we are staying offsite next trip), I think there is an unmistakeable sense of fun and excitement staying onsite. And we have never rented a car and have liked the WDW transportation.
have fun!
ps. If you ask this on the Resorts board you will immediately get about 9,000 replies telling you that your trip will be totally compromised if you stay offsite. It will be a great thread to make you feel good about a decision to spend the extra $$ and stay on site, but a terrible thread if you really want to keep an open mind.