It really depends on where you are coming from. Generally speaking no, renting a car is not recommended for visiting Cinque Terre. The villages are very small and pedestrian-friendly, and there is no parking available in the villages themselves. You will need to park in one of the nearby towns, such as La Spezia or Levanto, and take the train to the villages. The train is the most convenient and efficient way to get around Cinque Terre. The train stops at each of the five villages and offers stunning views of the coastline.
Coming from the US, Milan seems to be the obvious choice as it's a hub for international flights, however Pisa is also a good option and closer to the Cinque Terre National Park. Both Cities have trains that arrive directly at Monterosso al Mare, where the wedding venue is located.
Cinque Terre is a casual destination, so you can pack comfortable clothes, sneakers or hiking shoes, beach and casual wear.