I have been growing vegetables in raised beds for many seasons, also potatoes in large flower pots. I build a 1 x 1 m box about 20cm deep. 1 x1 is too wide to reach the middle, so I suggest say0.5 x 1 m and 20 cm deep. THe problem with a deep bed is to find sufficient compost to fill the bed. I fill my beds with compost which I make the year round. It does not have to be well rotted, just the top say 5 cm so that you can prepare a seed bed. I throw in spent flower pot compost, clippings and cuttings at the bottom, a few bags of anything that is bulky and cheap at the garden centre. I also add a good handful of fertilizer for good measure.
I have grown tomatoes, lettuce, radish, mache, okra, garlic, herbs,aubergines etc both from seed and plants. I find that squash etc take up too much room. I plant as thickly as possible, harvest early and try to keep a succession going...even if i loose some at either end of the seasons.
Homegrown vegetables give freshness which is the key to taste.