Originally posted by Dvitale
I have just joined a friend who has Nikon set up and she likes to go out to take pictures of nature. She enjoys to shoot whales, birds, dogs, horses and other animals. Most of her pics are at a distance due to necessity.
Much depends on the distance and the size of the subject.
If you are talking about a small bird more than 20m away, a 300mm lens is nowhere near enough. But for a medium-large bird within 10m, like this heron, it is.

(Taken with the K-S2 + DA-L 55-300, a $100 lens.)
With a large animal (e.g. a horse or cattle), 300mm is often more than enough. This photo was taken from a safe distance (with a K-S2 and DA 55-300 PLM) at 260mm.
If you are photographing whales on a cruise, they sometimes come close enough that a long lens is not necessary. I got this humpback with a DA 18-135 at 31mm.
And this one with the PLM at 108mm
But if you are photographing from the shore, you would generally need more than 300mm to get a worthwhile shot.
What I'd say is: start with your F 100-300mm and see how you go. If 300mm is adequate for your needs you could persist with the 100-300 until you are able to upgrade to the 55-300 PLM (or, if that is out of range, one of the screwdriven-AF 55-300 f4-5.8 models). As others have said, anything longer than 300mm (especially with autofocus) will involve a big jump in cost and weight.
I haven't used the F100-300, but in general these sorts of zooms do best stopped down to f8 (or even f11). Try using TAv with the shutter speed at 1/500th or faster and the aperture at f8 and let the ISO float up to 3200. If that isn't enough for the available light, try dropping the shutter to say 1/250th first; then the aperture.
Technique matters. I'd suggest reading this article and working on these skills:
Making the Most of Long Exposure Handhelds - Introduction - In-Depth Articles