I have had the 50-500APO Sigma aka Bigma for a few years now obviously this is the older model same optics but without any stabilisation and I believe the lens coatings have improved.
I have used it mainly on a D200 but now have moved to a D7000.
For the price the Bigma is very good value, its a tad on the soft side and lacks contrast in overcast or low light conditions but in situations with plenty of bright light such as I am sure you would have on safari it would work fine. I have used it mainly for air shows which does push it to its limits of perfomance as I live in the UK so dull days are the norm rather than the exception.
Overall its about the most popular lens at air shows as its a really good compromise between cost & quality. I have had the oppotunity to do a bit of AF fine tuning since moving to the D7K and its made a noticable difference as although you can't tune for the whole 50-500 range of the lens because I use it at between 300-500mm nearly all the time I set it with the lens at 400mm using a focus chart this gave me +5
The increase in CMOS & exposure performance with my new camera over the old D200 has picked up the lenses ablitity alot
This old image link I have attached was taken on my old D200 a while ago and is about a 40% crop at 500mm
IMO its not a bad lens at all.
To obtain the best from it, just a few hours practice & you will get suprisingly exceptable results. I reckon if animal work is what you are aiming for you should be able to get much better results than I can with planes as
1. they move slower
2. you wont have to deal with constant back lit subjects
3. on prop aircraft I have to keep to less than 200th and pan shoot, at such a slow shutter speed,handheld on what was on the older Bigma an unstabilised lens at 300-500mm means not that many keepers out of a days shoot
I personally think it would do what you want fine and without breaking the bank