To my knowledge there is not a shuttle to Vero. We've been to Vero twice. We LOVED it. (But then again, we are beach people and are happy for a week on a decent beach with good weather!). But seriously, we loved the resort and the staff. Can't wait to go back. We've just been using our points lately to try new things.
Definitely rent a car. There are some decent and relatively inexpensive restaurants within several miles. But as a PP stated, Vero is NOT like WDW. It is a small resort with not much around it. You really do need a car.
We've always flown into MCO. However, Melbourne is closer if there is decent airfare. Coming from Chicago, MCO and a rental car always are cheaper.
Have fun! Can't wait to return to Vero!