Well, you have plenty to ponder! You got Pigeon/Dove. Let's start with the fact that pigeon and dove are two words for the same sort of bird; dove is usually applied to smaller, lighter-colored varieties while larger, darker varieties are considered pigeons. Pigeons typically get a bad reputation as nuisance birds, scavengers and thieves, while doves are considered lovely, sweet, and a popular symbol of peace. These birds have very strong wing muscles and are among the strongest, most maneuverable fliers of all birds. They are among the most adaptable birds on earth, absent only from the Arctic, Antarctic and the driest Sahara desert. They have evolved little, going far back in the fossil record just as they are; this is THE bird, the foundation upon which the concept of "bird" may be built, the essence of "bird-ness". It is also the bird equivalent of human beings, which is never more clear than in our odd love/hate relationship and the fact that virtually every human quality is, in one way or another, projected onto them.
The most powerful word associated with this bird is HOME, in as many ways as the word can be thought of and interpreted.