The general rule for choosing a shutter speed when using a telephoto lens -- assuming you want tack sharp pictures -- is the speed of the shutter should be the reciprocal of the focal length, or fast. For example, if the lens you are using is a 300mm, the shutte speed should be at least 1/300th of a second. This guarantees that if the telephoto lens is hand held, the pictures should be sharp.
If the subject is moving, though, a faster speed should be used. I photographed this mountain lion in my summer babies and adults workshop in Minnesota, and I anticipated that the cat was going to jump in to the water. I used shutter priority and chose a speed of 1/1250th of a second on a 300mm telephoto because I wanted every hair, every drop of water to be sharp. Fortunately I had enough light so the ISO could be low. I used 400 ISO.