@plambers Panasonic and Canon have historically made the best affordable safari-friendly superzooms and Sony the best in terms of picture quality but a bot shorter on the zoom (really generalising)..You'll have to make a choice between image quality (1-inch sensor) and reach with the zoom. I'd assume that at least 50% of the extra reach is achieved at the expense of a corresponidng decline in image quality. You should look at capability in low light since you will be shooting very early morning and evening. So you ideally want either a constant f/2.8 or f/2.8-4 aperture on the lens or a very good high ISO performance - look for praise at ISO 3200, not merely "not bad". Any camera that noticably smears shots to deal with noise at high ISO should be avoided for safari.
One more thing is to decide whether you want a decent viewfinder or are happy to just look at the back of the caamera to compose your shots. Some cameras that have a viewfinder have such a poor viewfinder (i.e. can barely see what is going on) that they may as well not have one - you'd need to look to see that.
As for stabilisation, you should always get a camera that fits you well, so you can hold it steady. Five way stabilisation is good. Sony have the best current in-camera stabilisation system I think (they did last year but all changes so quick maybe they have been overtaken now) but I don't know if they put it in their superzooms. A viewfinder will help you to steady the camera as you press it against your forehead. I see people waving their camera around like divining sticks while they themselves are also swaying. That's not something any stabilisation system can handle. If in a vehicle a beanbag will make a noticable difference -again, if you keep it steady.Many safari vehicles have tables for beanbags now and so a little gorilla pos might be helpful too.
If you are yawning or screwing up your face as you read the above then upgrade to an HX300V or a Lumix FZ72 and save a lot of money. You'll even save enough to be able to afford another, really big upgrade if you find yourserlf getting keen enough to go off full auto sometimes.
And whatever you do, don't ask @amybatt If you follow her you will end up taking the one you have now and complaining about it for months and months.