I think that there's a recent thread on this subject that might help you.
For what you describe, you might consider a camera with shutter speeds of 125th and faster and a zoom lens. The faster the shutter and longer the focal length, the more likely you are to need something to brace the camera against to prevent shake so don't go too far with that.
A good compact would probably suit you but an SLR would be better. I use Canon but there are other good brands. Mine has, in addition to fine optional adjustments, some set combinations of shutter and aperture for various needs, such as fast moving chickens (!), and auto focus. I also use zoom to reduce the amount of editing I need to do. If your chickens like deep shade, a built in automatic flash would help.