There are very few things that don't do reasonably well in pots. Especially in the world of vegetables. But you do take on a lot of chores and expense that way.
When I lived in Missoula, I had a limited patch of sun and worked my butt off to get every little bit. I had all sorts of containers.
One of the biggest successes was tomatoes from a hanging planter. The vines would hang down six feet!
Getting the plant lots of sun and keeping the tiny bit of soil moist is the big challenge. I remember I ended up liking the pots that sat in a deep dish. I would carefully water everything a little less than the amount I thought they could hold and then top it off an hour later. I wanted the water to not pour out the bottom - because that would rinse away the nutrients.
Here's just one site with some basic information on container gardening. Googling that phrase will get you more.
Use the largest containers you can, preferably plastic or wood. Small ones dry out too fast and the roots can get too hot. Those plastic party tubs designed to hold ice and sodas are pretty good for shallower-rooted crops like lettuces. Be sure to drill or burn drainage holes in the bottom. (Small soldering irons -- $7 at Harbor Freight, etc -- are wonderful for making holes in plastic.)
One great way to water in a container is with an unglazed terra cotta pot that has had its hole plugged with hot glue: Fill a large container (half a barrel or so) with your planting mix, and bury a large (one gallon or so) clay pot almost up to the rim (leave 3/4") and set a saucer in the top after filling with water (so lizards and bees can't drown). Also water the soil thoroughly, then plant your plants or seeds. Keep the clay pot full of water. If the soil needs water, it will ooze through the pores of the pot. If it doesn't need water, the water will stay in the pot.
If you are putting your containers on a roof or balcony, it might be a good idea to use lightweight synthetic potting soil with some compost added, as it is lighter than regular soil.
I've heard that even corn can be grown in large containers, but you'll have to plant several in one container, as they are wind-pollinated and must be near each other.
I would especially consider things that can actually benefit from containers. carrots are one since they are picky about soil friability.Supposedly you can get monster yeilds of potatoes using containers because you can build the soil over the plant as it grows more easily and control moisture better. I have had great luck with tomatoes. both the varieties designed for containers as well as others. one 'sweet one hundred' in a container overwhelms me with super yummy grape type tomatoes that I could make my self sick eating! I like to position a container of those along a frequently used path or porch area so that I can nibble them in the daily course.
that is a lot of great information, but there is one thing that you need to remember when planting in containers..watering them. Make sure that your containers drain well, but that they will also hold a lot of moisture..sounds like that is contradictive, but it is not. Also dark pots heat up fast and light color ones reflect heat, terra cotta holds moisture well..and you can add a mulch to the top of the soil to keep in moisture. Also a good idea to warm up your water a little if it is cold before putting it on your plants..bre
Bloom where you are planted.