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The container needs to be stable enough to not tip over, hold adequate water compared to the size and number of the plants, withstand seasonal temperature changes and still look good!
Container Size
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Stability
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Shape (and volume) determine whether a container is stable enough to keep the plant from tipping over in wind as the plants grow. Square pots are the most stable. Traditional pots (sliced off inverted cones) tip over easily. Pots with straight sides like cylinders are more stable. Small pots may be "top-heavy" with plants tipping over more readily. Strap or anchor tall plants in place if they become top heavy. Watch for this problem on exposed balconies, rooftops and decks especially prone to winds. Look for a base broader than pot's height to minimize overturning if that is a concern. Consult with a building architect concerning weight limitations when placing heavy pots on balcony or rooftop gardens.
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Container volume affects maintenance.
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How big will the growing plants get? In general, larger plants need more room for roots. Is this a temporary display of annuals? Or is it a long-term display of perennials or shrubs? Will they need protection from fluctuating winter temperatures? Larger, thicker pots or insulated pots will do a better job protecting overwintering roots.
What are the watering needs of the plants? Shallow containers work well for succulents, because they need to dry out between waterings. Plants that require moist (well-drained) soil need a larger root ball to guard against drying out and reduce the need for constant watering.
How often do you expect to water? Given the same number and kinds of plants in the same location, and type of container, larger pots need less frequent watering than smaller pots. If you plan to go on vacation later in the summer, then choose a big pot or a big, self-watering pot.
The plant should look like it fits without being squeezed into the container. Never trim the roots to make the plant fit the pot unless you are creating a bonsai. The pot should be big enough and deep enough for the plant. Conversely, if the pot is much too big for the plant or the number of plants, the soil will have a tendency to stay wet longer and root rot is more likely.
Adequate pot size is especially critical when growing vegetables.
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Finally, good looks are important!
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Will there be groupings of different kinds and shapes of containers? How will they look together? Think about the colors and styles of the container compared to its setting? For visual and color tips, review the section on combining plants.
Tip to stabilize a trellis or plant on a hook in a large pot: Pour quick-set cement into a coffee can, set the plant hook base in the cement in the bottom of a coffee can. Once it is set, this can be placed into the bottom of a larger container before adding soil and plants.