Birds possess several types of feathers, but the ones that I use in painting are all flight feathers - most of these are secondary wing feathers, occasionally a tail feather, and on rare occasion a primary wing feather. The reason for that is their breadth and their strength. Flight feathers must stand up to wind pressure and give the animal lift and maneuverability.
Each flight feather has the same structure and anatomy: quill, shaft, down, vane ... the colorless tip of the shaft that lies beneath the skin's surface is the quill. Think of feather pens, it is the part that was trimmed and used for writing. Pick up a feather from the ground and you will see a ring above the quill, much like the cuticle where your fingernail meets with your skin. The longer the quill below that cuticle in relation to the size of the feather, the more powerful the flight of that bird. An eagle has a very long quill and a powerful sturdy shaft; the peacock's quill is rather short - he has just enough flight capacity to carry him across a field or up into the trees.
Image from http://globalflyfisher.com
Each feather when firmly attached and in use has its own blood supply. The quill is wide and tubular at the tip, allowing blood flow to feed and nourish that feather. As the feather wears out and no longer serves the bird well, the tip of that quill will pinch closed, cutting off the blood supply, allowing the feather to "die" and drop off. Molting occurs in stages, often after breeding season - the bird will not be without enough feathers with which to fly. During the molt, worn feathers in this transition can irritate the bird - the flesh will begin to itch. That's when you'll see the bird preening and pulling the loosened feathers to rid himself of the irritation. Occasionally you'll find one with a snip taken out of it... that's one that was bothering the bird and was probably still hanging on pretty good. It's disappointing to pick one up that's absolutely perfect, except for that chunk taken out of the top of it!
Now look at a discarded wing feather's tip. Does it taper to a point, like a pencil? That feather dropped off naturally. Does that feather, rather, look wide and open at the tip, like a drinking straw? That feather was very much alive and was pulled out of the bird. You might see traces of blood in that one, its removal was far from a pleasant experience.
One more important matter to keep in mind when selecting feathers - make sure you are using the plumage of domesticated birds, and not that of indigenous wild fowl. I am speaking strictly from a USA standpoint here, other countries may differ - there are many laws forbidding the use of wild feathers. I believe that nationwide you cannot pick up and possess a feather from any bird of prey. Eagle feathers are widely known to be illegal, but the same goes for hawks, owls, etc. It does vary somewhat from state to state, but in some states you cannot pick up feathers from any wild birds. Best to play it safe, stick with "barnyard" birds. Happy painting!