Leaf lettuce is always a good choice.
It is easy to grow and does not require a lot of sun (if you have a shaded space) and actually bolts quickly if it gets too hot.
Also, leaf lettuce can be grown easily in a smaller pot.
It is cheap to grow and expensive to buy at the supermarket.
Also, a vine-type plant can be good if you don't mind losing some of your balcony railings.
This would include cucumbers and some varieties of peas.
If you have lots of sun, most pepper varieties should work because they grow mostly up and not out.
Peppers like company and as long as the soil is warm and the temperature is up, you can fit a lot in a smaller space.
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Pretty much any of the dwarf varieties of vegetables will grow in pots - Thumbelina Carrots, those little round beetroot, etc...
Salad leaves are a great starter in any windowbox, and strawberries and tomatoes grow well in hanging baskets.
Your local garden centre will be able to advise, or get a seed catalogue and be amazed at the choice!
*Disclaimer: I work for a garden centre
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Grow what you like to eat.
Given your limitations though maybe start with herbs - like basil and rosemary.
They can be added to anything and trimmed/clipped any time.
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I have almost no land
but I am still able to grow a plethora of fruits, herbs, and veggies.
If you have the pots and soil, you can grow whatever your local area can provide based upon weather and sunlight.
I grow: tomatoes, strawberries, peppers, key limes, lemons, beans, lettuce, radish, catnip, onions, basil, spinach, pineapples, and much more herbs.
The small trees I have are in large garbage cans, and everything else is in pots with potatoes in the ground.
Good luck!
Just keep working on it and check to see what will grow well in your area.
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Some things that can work on a small area situation includes a variety of containers that can be used in different ways.
A way that has been succesful is the upside down hanging tomato planter.
If you can hang it five or six feet off the ground you will have good results.
Large containers such as 5 gallon paint cans can grow just about any vegetable or herb.
Earth Boxes are a good choice, and decreases maintenance.
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I currently live in a condo with a limited sized balcony.  Which vegetables work out best for a small garden?
What vegetables can be grown effectively in a small, urban garden?
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<vegetables><urban-gardening>
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Start off with herbs. You can try a climbing plant to grow up railings like cucumber or peas. You can also grow lettuce, peppers and any dwarf variety of plant. Try a tomato hanging basket. You should always grow what you like to eat.  A vine-type plant like cucumbers, peas, can be good if you don't mind losing some of your balcony railings. If you have lots of sun, most pepper varieties should work because they grow mostly up and not out. Pretty much any vegetables will grow in pots or 5 gallon paint cans. Salad leaves are great in a windowbox, and strawberries and tomatoes grow well in hanging baskets. You could start with herbs like basil and rosemary.  
Leaf lettuce is always a good choice. A vine-type plant like cucumbers, peas, can be good if you don't mind losing some of your balcony railings. If you have lots of sun, most pepper varieties should work because they grow mostly up and not out. Pretty much any vegetables will grow in pots or 5 gallon paint cans. Salad leaves are great in a windowbox, and strawberries and tomatoes grow well in hanging baskets. You could start with herbs like basil and rosemary.   You should always grow what you like to eat.  