I think you need to state what type of island you want. If you want luxurious hotels and upscale restaurants, then Phuket and Samui are for you. If you want more local ones, then there is much more choice. Although Samui and Chang are easy to get to, the Samui and Trat airports are privately owned by Bangkok Airways, and therefore priced as a monopoly.
Driving outside of Bangkok is very straightforward. Just make sure you have an international driving license. On my next visit in May we are going to drive to Hua Hin for a few days, then up to some national parks near the Myanmar boarder. Last time we flew to Chiang Rai and did a great road trip of the NE - Highlights were the boarder roads above the Wild Boar Tham Luang caves. Having a car gives great freedom to roam near or far from the sea.