Sabi is a good place to start but check out the accommodation options. You will need a shorter zoom there, such as a 70-200, for most of the time as the open vehicles get closer to the wildlife.
Keep your eyes open always too and be careful where you are walking....came out from breakfast last year and almost stood on a Green Mamba by a small pond.
Sabi and other private reserves in that area are on the edge of The Kruger Park and known as franchises. These places invariably go off road. At Sabi for the first time, our lady driver (nicknamed Schumacher by the locals!) got a radio call to confirm a leopard sighting. Direct route used, flattening small trees and bushes etc and we ended up quickly parked 10 metres away from the big cat. On the first night drive there, I could have stroked a lion as it strolled alongside our vehicle!
Ngala is another option, further North. If you get the chance, use the light aircraft fly in service from Mpumalanga airport. Amazing views flying in low and more than likely a herd of elephants on the landing strip at Sabi. Be careful of baggage weight limit though.
In the SANPARK reserves like Kruger and Pilanesberg, the safari vehicles generally stick to the road network so your 200/400 (or longer) will be ideal. This is where you are likely to encounter bigger groups of vehicles that will crowd a sighting and make good shots more difficult.
The Masai Mara is an entirely different experience and there your longer lenses will be most useful but do have something wide for landscape work.
Safaris are an awesome experience! I can also recommend going on a walking safari for one day at least.
Last couple of suggestions.
1) Consider using a local travel company such as go2africa.com who I can highly recommend. You can talk to a real person, via email or telephone and their local experience is invaluable, especially if things go wrong whilst you are there. Awesome service. No doubt there are others.
2) Think out of the box. Try to fit in a short trip to Kleinbai which is near to Hermaneus, about an hour's drive North of Capetown, to go out on one of the shark boat trips to see Great Whites at close quarters. Recommend shark lady.co.za who was the pioneer of cage diving in that area (you can stay on the boat if you prefer) ... This shot is a scanned image of a print from an early trip there and was using a 10D or 20D with a wide angle 10-22...... I could have kissed this one as it was so close.