It is seldom that you will be able to fit landscapes and animals (I assume wildlife?) into the same lens requirement. Landscapes generally are with shorter focal length lenses, such as 17-70mm, wildlife you’ll require longer lenses, such as 150-400+ mm. Yes one do have the 18-200mm type lenses, and depending on your requirement for image quality they can do the job, but expect less than perfect end results. Here the Sigma 17-70 will work nicely, and serve as a general all-round lens.
There is also the plethora of 70-300mm lenses, some better than others, of teh better ones the Canon 70-300 IS USM and Sigma 70-300 APO comes to mind. Also have a look at the newer 120-400 Sigma lens with OS and HSM focus, seems to be OK for a mid-range performace lens.
The stabiliser will only help with low light, slow shutter speed photos of stationary subjects, on a 300mm type lens its a nice to have, not a necessity. Support for the camera/lens playes a major role, ie will you be using tripods/monopods/bean bags? – then stabilisation is not really going to help you much.
Budget playes a major role – without this we can only recommend the range on which to look for, specific models can range in price from R3000 for entry level to R35000+ for pro series lenses.