Karen,
Since you quoted your price range in $, I assume that you are located within the USA.
It is agreed by many bird photogsphers that virtually the best Bird and Birds in Flight lens is the 400mm f/5.6L lens. Granted, it doesn't have Image Stabilization but, it is razor sharp wide open and the auto focus is amazing. Shooting at ISO 400 or slightly higher @5.6 will give you a shutter speed fast enough to stop the bird and to nulify any camera shake.
On a sunny day, ISO 400 @ f/5.6 should result in a shutter speed of over 1/3000 of a second (if your camera goes that high). Most of today's DSLR cameras can provide very clean image quality at ISO 400 or even a bit higher.
The lens, used on eBay generally sells for right under $1,000 which is within but, at the top, of your budget. Here are some sales on eBay from the past few weeks.
http://www.ebay.com …=0&_sop=12&_dmd=1&_ipg=50
I often use this lens either on a tripod or on a monopod.
Unfortunately, I am not a birder so I have no bird images to show but here is a hydroplane racing boat crossing my field of view at well over 100 miles an hour.

IMAGE LINK: http://rpcrowe.smugmug.com …36168266&k=2JSDf&lb=1&s=A
Sometimes when shooting birds, especially birds in flight against a blue sky, it is difficult to find the bird when viewing through the eye level finder and totally mpossible when trying to view using the LCD. I have an old gaget which can help. It is a sportsfinder which was once part of a Navy Topcon 35mm kit that was issued to Navy aviators. This little gadget fits onto the camera hotshoe and makes following a moving subject quite simple.
IMAGE LINK: http://rpcrowe.smugmug.com …49079880&k=Sk7CZ&lb=1&s=A
You can occasionally find sportsfinders of various types on eBay. However, some of them have become collector's items and are often expensive...