Hi Andrew,
You should enjoy Vava'u - it's a great spot to visit and the people are excellent. Dave's recommendations regarding tackle are basically sound. I don't think you need to go beyond 100lb braid. You should get in touch with Kurt Carlson who is a member of this forum. Kurt lives on Vava'u and is without doubt the expert on popping for GT's in that part of the world.
You will find that there is a need to get beyond the easily accessible areas as the Tongans have a habit of keeping what is caught to feed their families, so the further you can get from populated areas the better your results will be.
We fished with Kurt for a week earlier this year, essentially popping for GT's, and found that whilst GT's are there to be caught the average size is under 20 - 25kgs. There will be bigger fish naturally, but the further out from the main island you venture the better your chances.
Land based is a viable option, depending on weather, but local knowledge and guidance will be essential if this is your intention.
You would be a lot better off to work with Kurt who has a boat and rely on his knowledge and ability to access the areas that can produce.
The majority of the guides/charter operators who work Vava'u are very focused on blue water trolling for billfish. They do this well - their results with marlin speak for themselves. However, if popping for GT's is your intention, get in touch with Kurt.
Don't ignore the general fishing opportunities that exist in Vava'u though. There is some of the most enjoyable light tackle fishing for mahi mahi and small tuna you could hope to find.
cheers,
Malcolm