Oh cute! You have lots of choices. English boxwood looks nice, yew, blue spruce, many evergreens would look good year around. My choice would be one of the smaller Japanese maples, perennials or flowering shrubs. One of my barrels has fountain grass with two colors of sweet potato vine, but that's not really year around. Anyway, whatever you decide is sure to look great, post a picture when it's done!

Wavy rims will tend to distract from any planting combinations chosen

Just to give you more ideas, I have some half barrels planted with dwarf apple trees and Sedum rupestre 'Angelina' below.

But do you replant them some time or they stay in the same soil all the time?

Surprisingly, I haven't need to and they've been in for probably 12 years. I am finally going to replant the trees this fall, because the bottoms of the barrels have finally gotten too rotted and the soil level has sunken down too far.