It depends upon what growing zone you are in. That will tell you what vegetables and types of vegetables like early girl tomatoes rather than a different type of tomatoes, etc. grow best in your area.
Which zone are you in?
It also depends on the length of your growing season, generally the further north you are, the shorter the season.
So you would have to start them indoors to make up for a shorter outside time.
The ones you like to eat! Do you know what zone you are in?
Lettuce and other salad greens grow great in a container! So do carrots (in a wide and deep container). You can even grow potatoes in a deep pot!
every type can be container grown as long as size is ample for the veggie/fruit type and their root system.