If you want to grow tomatoes hydroponically, a dutch bucket system would be better.
Tomatoes require a lot of root space so an 60 to 75 liter container would be best (16-20 gallons in case my math was wrong)
You would run the pvc tubes with small holes drilled in the tubing over a row of buckets filled with cinder or hydroton.
The buckets would sit in a long tray that is slightly tilted toward a drain hole. The drain returns to the reservoir.
This system can be run hydroponically or you can use aquaculture with tilapia or catfish to provide some of the nutrients. Fish cannot supply all nutrients so you would still need to supplement with approved organic fertilizer and you may need to add calcium and iron for some crops. You will need to source out what is acceptable where you are for aquaponic culture.
In an aquaponic system you will be limited to what you can do for pest control so sanitation will be important.
In hydroponic culture you have a little more leeway, but with many plants in a closed environment, pests will also be a problem since there won't be many predators either, so sanitation would still be important.
Heat resistant tomatoes will be necessary in summer even with a climate controlled green house.
Cherry tomatoes will be more resistant than larger tomatoes.
Sungold, sun cherry, and Matt's wild cherry are very good.
Larger tomatoes with good heat resistance Arkansas Traveler, Big Beef, and Heatwave II are the only ones I have tried.
In a greenhouse with tomatoes closely spaced they will need to be trained on a string trellis and pruned.
It is a big investment so I would start small especially if you don't have a lot of experience or space.
This is an instructible for a simple dutch bucket system. But a five gallon bucket will only support a small determinate tomato. You would need a larger bucket for a big tomato. We use 65 liter grower pots they do not have a cover but they do have a tray that drains to a reservoir and pvc tubing to deliver water in cycles.
http://www.volusia.org/core/fileparse.p ... Bucket.pdf
Happy gardening in Hawaii. Gardens are where people grow.