If you are trying to keep pest out you can put a wire screen at the bottom of the bed and put cardboard on top to that to block weeds. Make sure your bed gets at least 6 hours of full sun for veggies. If you are planning to plant something large like tomatoes, put them in 18 gallon or 20 inch pots instead and make a cage with concrete reinforcement wire. My cages are 7 ft tall by 6 ft long. Caging means you don't have to do as much pruning. 6 inch diam. CRW allows your hand to get through the wire to reach the fruit. If you put tomatoes in an 8x3 bed and you have a 7 foot trellis on the north side, you could probably get 4 tomatoes in there. If you use SFG spacing you can get 8 but you will be pruning off all of the side shoots and most of the fruit. Pots use potting soil, a 2 cu ft bag of MG will fill an 18 gallon pot 3/4 full. I use part of a second bag to fill it within a couple of inches from the top since potting soil settles. I add 1/2 cup of complete starter fertilizer and I supplement at flowering, first fruit, and monthly thereafter. You could add all of the fertilzer as a band about 4-6 inches down in the beginning. 2 cups citrus food plus micros or 3 cups organic. 8-8-8.
If you have a local composting facility and a truck. Check with them about getting a vegetable garden mix. Mine costs about $48 for a cubic yard if you pick it up yourself. Delivered it is $240. If you tell them the dimensions of the bed or you can do the math to figure out the volume of your bed. I would also make sure your bed is reinforced on the outside if you made it of wood to handle the weight of wet soil. If you made the bed with concrete tile and reinforced it with rebar and pack the cores with stones or soil, it will hold.
If you are building the garden now and plan to use it right away, you can make a lasagna bed, but you will have to top it with 4-6 inches of good garden soil or potting mix and fertilizer (with added nitrogen) to use it right away.
Otherwise Mel's Mix works
1/3 good garden topsoil
1/3 compost from multiple sources
1/3 vermiculite, perlite, coarse sand (builder's sand), or cinder for drainage.
Don't use cinder if you are going to grow root crops like carrots.
Blend it all together and fill the beds. You still need to add fertilizer. If you want to be organic your topsoil will have to have a lot of organic matter in it to get enough soil microbes. Bagged "topsoil" usually is just dirt. It is better if you can get soil that is loaded with organic matter like the first few inches of soil in a forest, or soil near bodies of fresh water or if you can get soil from the yard if it is rich in organic matter like someone's established garden. Even if you cannot get the volume, what you really want are the microbes in that soil to seed your bed. You can also add vermicast which has live organisms and use EM to stimulate growth. Over time as you add organic matter the soil community will build up and all you have to do is keep adding organic matter and fertilizer.
Organic in the first few years from a scratch bed is not going to yield as much as a bed fertilized with proper amounts of synthetics. Get the soil tested after it is blended to find out how much fertilizer you need to add. If you want to do it organically ask for organic recommendations.
I am not 100% organic, I add compost to feed the soil and to release bound phosphorus, but I do not like to use animal based fertilizers and unfortunately they are the best source of organic nitrogen. I do get soil tests and I only need nitrogen and sulfur to amend the alkaline beds. The best choice for me is sulfate of ammonia. My soil does not need phos, potassium or calcium for years. You can call your local master gardener and get information on getting a soil test. A soil test from my local university for basic pH and nutrients costs $25. I've saved more than that by not buying fertilizer I don't need and using less of the ones I do.
Happy gardening in Hawaii. Gardens are where people grow.