I think planters should be stuffed with annuals or perennials that are treated like annuals, since the soil should be changed out every year. You can use a wide variety of annuals, providing interest and color all year long. We can't really help you with selections until we know how much sunlight (in terms of hours per day) this planter will receive.

In my location, candytuft blooms for a pretty short period of time, but it may be different where you are.

Is this box on the ground--a boxed in flower bed or does it sit alone above ground? How much sun does it get?

I hope that when you say evergreen you don't mean shrubs or trees. You don't have enough room for either. 1 foot is not wide enough to grow anything but a single row of smaller plants with small root systems.

You can always 'cheat'. If you want to have seasonal patches of colour in your box use potted plants and snug them into the soil in the pot. Water and feed as usual.

Low maintenance and trails: hmm. Variegated ivies are possible. Verbena. Sempervivums but you need patience for them while they increase. Echeveria, if you have a sheltered area.

Temporary trailers - tuberous begonias - or ordinary semp begonias for upright colour in leaf and flowers. Semi shade suits them best.

Shady? Impatiens is quite tolerant so long as you don't treat them like camels! (They appreciate watering...) So are the Tradescantias and Setcraesea but they are all frost tender. You could add in Davallia fern, too, which looks pretty but is tender.