Every guide here names varieties bred for containers and gives a minimum pot size in gallons, so you can tell at a glance whether a crop will fit the space you have.
What's different about vegetables in pots
A bed holds a lot of soil, so it forgives a missed watering. A 5-gallon pot holds much less. Three habits cover most of the difference: size up (the sizes in each guide are minimums, so go bigger where you have the room), feed little and often (nutrients wash out every time you water), and mulch the surface to keep the roots cooler through July.
What to grow first
Lettuce, bush beans, radish and chard are the forgiving ones. They germinate quickly, cope with a missed watering, and give you something to pick within about six weeks, which is the fastest way to enjoy this. Tomatoes, cucumbers and potatoes are worth the wait, and they go better once you have a feel for how quickly a pot dries out.