Some overriding considerations are
(1) what do you like to eat?
(2) how do you plan to use the vegetables?
(3) how much work do you want to do?
If you like all vegetables equally, then certain varieties of beans, cherry tomatoes, and summer squash might give you the most return. It's a good idea to research specific varieties you are considering to see if they are known for high yields in your climate. These varieties were hugely productive for me in my cool-summer, long-season climate: Sungold, Sunsugar, Tommy Toe, Galina's Yellow, and Fox Cherry. I prefer pole beans rather than bush beans, because pole beans have to be planted only once, and they produce all season. Productive varieties for me include Blue Coco, Helda Romano, and Scarlet Runner. Bush beans might be a better choice for canning, because they tend to produce all at once, and you have to replant at regular intervals. Vining summer squashes are a good use of space if you can trellis them and use vertical space.
If you like some vegetables more than others, then the best vegetables to grow are the ones you like to eat. I like most plants, but I vastly prefer eating kale rather than lettuce or chard. In my gardens, I pick a few leaves here and there, and then the lettuce bolts (goes to seed and gets bitter), so I've learned lettuce is a waste of space for me. Chard is pretty, but I don't often eat it. But I eat bagsful of kale all year round, so any kale is an excellent use of space in my garden. If I could grow only one vegetable, my choice would be kale because it's productive year-round and I never get tired of eating it. It's also one of the most nutrient-dense foods, and I can pick exactly the amount I need. (Or rather, instead of buying a small bunch at the store or farmers' market, I can pick a grocery bag of kale.)
With some extra work, you can extend your season in both directions by using row covers, cloches, and other ways to protect your plants. It does take a lot of extra work (using walls-o-water and bubble-wrapped cages, restaking during windstorms, reinforcing the protection for unseasonably cold nights, etc.) and in my climate I can push the tomato harvest maybe a week earlier for every 2-3 weeks earlier that I plant them, so it's not a huge gain. If I had a greenhouse, I could try to extend the season even more.
But starting seeds to anticipate replacing a harvested crop is an easy way to make the most use of a small space. For instance, if you anticipate that your bush beans will be mature in a couple weeks, you can start new seeds in 6-packs so that they will be ready to go into the ground when it's time to take out the exhausted crop.
This article has a good discussion of how to decide what to grow.