It is common for people to put a bed along a wall or fence but it is often a mistake. Been there, done that. I built my bed with hollow wall tile, that was dry laid and stabilized with rebar and stones in the tiles topped with soil for planting the tops or cap stones. The tile works fine. However my fence is a 6 ft hollow tile wall. It faces east but because of the wall there was shadows cast on the bed till 10 a.m. The sun heated the wall and most of the plants grew tilted away from the wall. Only the vanda and night blooming cereus actually clung to the wall because they don't mind a hot wall. Cleaning the bed out was hard because I did have to go into it to clear it. Now I only use it for potted plants, mostly citrus trees. If it was a permeable fence the plants would have ended up in the neighbors yard.
A better plan is to move the bed out at least the height of the fence away from it 5-6 ft. That will give you a maintenance path all around the bed. A 4 ft wide bed can be worked from two sides. You can put a border bed or turf along a chain link or open fence but you still need for it to be able to be maintained so it won't encroach on the neighbors yard. Depending on your relationship with your neighbor, I would not plant veggies along the fence line because you don't know what your neighbor is using in their yard, so non-edibles and plants you won't miss can be planted there. I like using hollow tile because it is durable and will not rot. I live in Hawaii where wood in the ground will be eaten by termites or rot from the rain. If you build it 2 hollow tiles wide and two tiles high you will have a about 4 ft wide bed more or less. The tiles that form the long side of the bed will make it a total of 3 tiles wide (approx 4ft if tiles are 16 inches long). I would make the beds 8 ft long and you may be able to get two beds along that length. 8-10 is a comfortable length to work with because otherwise you would have to walk through the bed or go the long way around them. If you put two rows of beds in parallel to each other you can have 4 beds in a 10ft x 20 ft space.
Having different beds can be helpful for rotation and for plants with different needs. Tall plants like corn, okra, tomatoes will take up the entire space and have long maturities. Greens like lettuce, Asian greens, spinach have short maturities of about 50-70 days and they like similar conditions so it is easier for them to be in the same bed. They are short plants so would be blocked by the larger plants unless that is what you are going for. Intermediate maturities and larger plants like cucumber (on a trellis) zucchini which takes up a lot of space (36 inch circle), cabbages, squash, ice box watermelons, beans need more room
Some plants will need a trellis so they are best in a bed that is farthest to the North and the bed should have a permanent or foundations to accept a trellis. If you want winter protection to extend the season a bit longer. put in anchors so you can make PVC hoop houses for row covers.
I have a CRW trellis for my tomatoes. But when the tomatoes are taking a break, I use the trellis for beans, peas, and gourds. My home veggie garden is small it is an 8ft x 16 ft oval. It was a rock garden that was converted after we bought the house. I use stepping stones to divide it and provide a pathway, but walking in it is unavoidable. If I plant corn it can take up half the garden space. I usually try to keep smaller plants in the garden like cucumbers on a trellis, bush beans, bok choy, tatsoi, Swiss chard, spinach in the cooler months in half the garden. 5 broccoli plants will occupy half the garden space from September to March. Corn will occupy it the rest of the time.
I keep the tomatoes in pots outside the garden because they just take up too much space. I also plant longer lived plants like the herbs and peppers in pots that are around the veggie garden. I grow ginger in a large pot and citrus trees in pots to keep them small.
I grow the gourds and squash vines at my community garden since it has more room to sprawl. I grow carrots, beets, asian greens, mandarin, calamondin, papaya, and a lot of weeds there.
My house has an acidic soil and fewer pests so it is better for tomatoes and plants that need to be watered or picked more often. The root crops like carrots, beets and daikon do better in more alkaline soils and with less nitrogen. Plants at the community garden need to be resistent to disease and pests; live on rain and deep watering a couple of times a week .
Happy gardening in Hawaii. Gardens are where people grow.