I think your best bet would be the brand new Canon Powershot SX40 HS. It has an astounding 35x optical zoom or a 24mm-840mm eqiv range. This camera is brand new and was announced as shipping at the end of September 2011.
As for the shooting speed - this camera has two options. You can shoot at a continuous 2.4fps until you fill the memory card. Or you have the option of a "High-Speed Burst HQ" that will shoot 8 images at 10.3fps.
On top of those features that you are requiring, the camera has what Canon claims is 4.5stops worth of image stabilization, which will come in handy when you are out at 840mm!
This camera will be the best compromise that offers a great range, fast shooting speed, ease of use, in a small package, and at a decent price.
If you do require the highest quality, and apertures that are beyond the scope of a camera/lens of this size, you will have to look at professional grade lenses in the 70-200mm f/2.8 or 300mm f/4 range and up.
I apologize for this sounding like an advertisement - but really some of this new technology in point and shoot cameras is quite amazing.