Herbs do well in containers peppers, cilantro, basil, mint (must be in containers, and green onions).
You can grow almost anything in containers even tomatoes, but they do require a big pot. Tomatoes do need a lot of water so I do grow them in 20 inch pots. They just take up too much space in the garden. I have also grown them well in 18 gallon rubbermaid totes that were made into self watering pots. It solved the need for water issue. I had a 5 gallon reservoir and fruiting tomatoes can drink up to 4 gallons a day.
https://www.postoilsolutions.org/documents/Earthbox.pdf
Except for the herbs, I would rather uses larger pots as they do not dry as fast and I can get more in them.
Corn takes up a lot of space in the ground and the container. Squash can be trellised or allowed to sprawl outside of the garden. Zucchini takes up a big space in the garden I plant that in the ground outside the garden bed.
Broccoli is a slow grower and needs wide spacing 24 inches so I put that in the garden but I plant smaller things between them like beets,, spinach, and lettuce that will be harvested before the broccoli shades the space.
Nearly all of the vining crops will take a lot of space if you don't trellis them. Of all the vining crops, the one that is easiest to trellis in the garden are cucumbers as the vines grow tall but are not as rampant and the fruit is not as heavy as the melons and squash. These other things I like to plant near the fence and have them crawl on that or you would need to consider a very strong trellis. I still could only get one or two vines on that.
I have grown cucumber, tomato, peas, beans, jicama, and ginger in pots. I also grow taro and long ago I did grow sweet potatoes in pots. My pots are 18 gallon pots and tree pots that are big and deep. The ginger can be grown in 5 gallon buckets. Peppers in 7 gallon pots (tabasco peppers live more than one year). The 18 gallon containers are usually used for tomatoes and I have a trellis of CRW just for them. I have 3 pots on a 10 foot CRW tellis 7 ft high.
I have planted up to 9 beans or snow peas in one of the 18 gallon pots, and 3 jicama. I use a tree pot for the ginger, they need to be in nematode free soil, so I use new potting soil every year. Taro are also in pots they need a five gallon bucket each, and they are usually planted singly or the corms will be smaller. I have been able to grow cucumber and beans on a tomato trellis (the commercial kind, they really aren't very useful for tomatoes), bush beans do not require a trellis.
I can only grow the heavy squash (long squash, winter melon, chayote) on a heavily reinforced fence or trellis.
I have an overhead trellis that looks like a tent frame. The posts are fence posts and the roof is made from conduit tubing (because it could be bent into shape, and CRW. The sides are conduit and galvanized 1/2 pipe. It can hold a couple of upo squash vines. Upo squash is the most productive for me and will produce 20 or more fruit. I have a squash now that is sprawling in my community garden that is climbing my fence and the chayote on the side fence.
When the trellis is not in use I can plant corn or other things that need the sun. When the vine covers the trellis I can plant shade tolerant plants under it.
I've put together a list of plants I want to grow, and there's a whole lot more here than I can fit in my little bit of space, so I was hoping to extend some of it by planting some of these in containers and set them on a big wire shelf thing I have in my yard near my garden. 
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