The choice of lenses on the market is truly impressive, and this makes it difficult to know where to start. You'll have a good idea what quality to expect, and the telephoto you choose may be more compatible with the other lenses in your outfit. Lenses from the same manufacturer often take the same filters, resulting in a considerable savings. You may also find that the similarities in terms of focus and metering make them easier to use. A lens with a long focal length is an absolute must for pursuing wildlife, but you may immediately find yourself with a case of sticker shock.
Long lenses can be expensive, so it's important to know what features are most important.
Many wildlife photographers consider 300mm too short and prefer to work with a 400mm lens. There are some good zooms on the market also, but keep in mind that high-quality zooms are often very expensive. They also tend to be much heavier than prime lenses, which makes them harder to hand-hold and lug around in the field. There are products that help anchor these long lenses while also assisting in tracking your subject. A tripod is useful, of course, for mounting your camera when you won't be moving around a lot.