The thread below yours gives a few clues - the only other thing to say is that most video cameras in your price range will probably not have a seperate viewfinder just an lcd screen which makes tracking moving and flying birds in bright sunshine somewhat difficult.
The Panasonic SD900 (which does have a viewfinder) is being sold on Amazon reduced to be within your price range and is an excellent camera, however the lens only zooms out to the equivalent of 428mm which may fall short of what you need.
The cheaper SD90 gives you the equivalent of 730mm which is probably closer to what you are thinking of but at the expense of quite a few features including the seperate viewfinder.
The even cheaper Panasonic SDR-S50 gives you the equivalent focal length of 2625mm, but at the expense of losing HD recording as well. (But very cheap and fun to use)
To get the optical performance of the SDR-S50 in HD you are talking really big money.
N.B. for really long focal lengths forget about IS and buy a tripod.
I believe the SD900 has been used in a tv programme, however, excellent quality is no good if the subject is too small to see properly.
As you may gather looking through the recent threads most folks seem to be settling for something like the middle of the (consumer) range such as the SD90.
Don't forget to budget for a spare battery and a class 6 or better storage card if you are buying into HD.
The trouble is that you won't really know what you want until you have tried it for a bit.
A couple of reviews for you N.B. lots of people produce good videio cameras as well as Panasonic - its just simpler sticking to one manufacturer when talking about typical features.
http://www.techradar.com/reviews/cameras-and-camcorders/camcorders/panasonic-hdc-sd900-928795/review
http://www.techradar.com/reviews/cameras-and-camcorders/camcorders/panasonic-hdc-sd90-928756/review