Your vegetable plan is mostly the same family solanacious tomatoes, peppers and eggplant. You also had carrots outside the plan. The solanaceous are usually warm season and the carrots are cool season. Carrots don't like it much past 70 degrees and the solanaceous don't really get started util it gets that warm.
It is ok to plant the same family in a bed but you need to be careful because the same family will mean the same problems are likely to show up like diseases which could possibly transmit to other family members and they would share the same pests. As long as you don't have any serious problems and you can keep up with the pest control it is o.k. Ideally if you have 4 beds you want to rotate the family to a new bed every year and plant a different family in the former bed preferably one that has different pests and diseases to keep that from getting worse year after year.
I would make a plan for the cool weather crops and a second succession plan for the warm season
warm season: tomatoes, eggplant, squash, melons, beans. These are plants that like temperatures 70-80 degrees
cool season crop: some of them will tolerate a light frost temps 40-70 degrees. Kale, carrots, beets, spinach, broccoli, cabbage, Asian greens, chayote, faba beans.
The best plan would face south. I know you said you only had a west face. How much full sun does the yard get? You need 6 hours of full sun. You want to site the garden so that it won't get shadows from trees or structures for at least that much time. The taller plants can be on the north end of the garden and the shortest plants on the south. You can hide some cool season plants between the taller ones to create a microclimate for plants that can handle partial shade. Beds 4 feet wide with access all around is best for maintenance without having to walk on the bed. Length can be what is comfortable,but most people don't want to have to go all the way around a very long bed so 10 ft is a good place to but a break in. 10x10 is a good sized garden, but you would have to walk in it to harvest, weed and plant. 3 ft would be a good sized pathway and wide enough for a wheelbarrow. Put down some weed cloth and mulch in the pathway to keep the weeds down and keep it looking neater.
I know where you are putting the plants but I cannot tell from the plan the direction Where will the sun be coming from? It helps to know that to place the tallest plants on the farthest north corner so they won't shade the shorter plants. I'd put all the tomatoes together since they would be about the same height next the cukes and then the eggplant south of the tomatoes since they are the next tallest plants and bush beans or peppers in front of the eggplant. Tomatoes and cukes will need trellises so having your trellisess and trellis plants in the same place just makes sense. Other things you could use the trellis for would be beans and squash as alternates. Include in the build out some trellising system. CRW panels and posts, cattle panels or "T" or upside down "U" posts all make good trellis structures, but they are more permanent than other types of trellises. You can also use cages which would have to be anchored.
I like that you are including some flowers and marigolds because they do act as trap plants and will also attract some beneficial insects.
When you do your plan you can block it out on graph paper so you know how many plants will fit in the space. You can use square foot garden plan as a guide for minimum spacing and maximum production. I find the spacing a little too tight and plant fewer in a block . I give tomatoes a three foot circle (I use cages ) so in 10 ft I only have 3 tomatoes for example. Cucumber on a double stacked tomato cage can go with a foot. I can plant 9 beans or snow peas inside a tomato cage. I also have space issues so I interplant and do not leave rows. I underplant tomatoes and eggplant when they are small and don't use all of their space yet with a short crop like cilantro or lettuce. They short shallow crop will be harvested by the time the tomatoes need the space. My garden is also small and oddly shaped. It is what I inherited so I have to walk in it. I use stepping stones in an attempt not to stomp on the plants. Sometimes I am not successful at that though, it does help to have the stepping stones. I actually try to keep big plants out of the main garden. I have aloe which became temporarily permanent and a Jamaican orgegano pot that went to ground already crowding the space. One of these days I will have to evict those plants and find somewhere else for them. I grow tomatoes, eggplant, and most of my peppers in pots outside the garden along with ginger, taro, and herbs. The herbs are in pots because they tolerate them well and some can be invasive. Taro and ginger are easier to harvest if they are contained. Potatoes could also be grown in a large pot or barrel. When the plants are young, the pots are closer together, as they got older, I put them in larger pots spaced farther apart and smaller pots between them. It give me more control over spacing for better air circulation, but they need to be watered almost daily.
This is a good website for learning about vegetables, when to plant, they have a free square foot garden planner and planting guides including spacing requirements. you don't even have to have a row garden. There are other designs like a hub and spoke garden, keyhole, or "L" gardens, free form, which can be planted to be more aesthetic if you choose the right combination of vegetable and ornamental plants.http://www.vegetable-gardening-online.c ... ayout.html
The farmer's almanac planting dates by zipcode allows you to enter your zipcode or city/state and get a planting calendar for the year based on your last frost dates.http://www.almanac.com/gardening/planti ... /Knoxville
You can be inspired by a bunch of free vegetable garden plans that you can use as a starting point and substitute different plants that would take up about the same space. http://www.sunset.com/garden/fruits-veg ... en-plans-0http://www.bhg.com/gardening/plans/vege ... rden-plan/http://www.gardeners.com/kitchen-garden ... ed-gardenshttp://gardenplanner.territorialseed.co ... plans.aspxhttp://www.mysquarefootgarden.net/
It is wise to start out small with a small a limited number of species. Do your research and know what grows best in your area and what cultivars will do best for you. For that your local extension service will help you a lot.https://extension.tennessee.edu/publica ... /PB901.pdf
You can always ask your local master gardener plant questions specific to your areahttp://knoxcountymastergardener.org/a/i ... r-gardener
for anyone else seach (city/state) + master gardener (look on the website for "Ask a question". Some sites tell you where the plant doctor booth's are or their office phone.
If you want to learn about a specific vegetable to grow in your area you would search for plant (tomato) + (state) extension service. You will get specific advice on when to plant, how to grow, the common pest problems and usually recommendations for cultivars that are known to do well. After you get the basics down, then it you can be adventurous and try other ones that may taste better, but be more challenging to grow.
You want to succeed so make it easy on yourself. Start with the simple bullet proof stuff first.
Beginning a garden is a lot of work just planning, killing the weeds or grass, laying out the beds and planning how you are going to water it. There needs to be a committment to work the garden as well since there is a lot to do between planting and harvesting. There's a lot of weeding, scouting and controlling pests and disease in between. You need to be able to commit 3-6 hours a week. Putting in some kind of irrigation system and timer really cuts the workload down a lot.
Happy gardening in Hawaii. Gardens are where people grow.