We like the Big Island best for a lot of reasons:
- Probably the best snorkeling (but plenty of good spots on other islands)
- Variety of scenery
- Not much traffic (outside of downtown Kona)
- Some great activities that are only on the big island (Volcano, Manta Rays
However, I don't know that I'd recommend it for a first visit. There aren't as many beaches and there are only a handful of hotels that are on really nice beaches (Mauna Kea Beach Resort would probably be my first choice).
A lot of people don't care for all the volcanic rock everywhere and expect more tropical surroundings.
Because you'll want to check out a lot of sights, you'll probably spend way more time driving than you would intend to on vacation.
I'd probably go with Kauai for the first time. You'll get a lot of the tropical sights you'd expect, and there are great beaches nearly everywhere. I'd stay near Poipu — they have great beaches, plenty of sun, and not much traffic (unless you are headed to the North Shore).