Kglagadi is my favourite park. I think I've been12 or so times. Only the last 2 have been in a 4x4 - the others were in a tiny hatchback.
You will be more comfortable in a 4x4, but it's not essential. There are a few roads and 2 wilderness camps (Bitterpan and Gharagab) that are only accessible with a 4wd - you just won't go there. Having a higher vantage point is an advantage - especially around Nossob where the road verges are very high. In some stretches, you won't be able to see in to the river bed from a small car. The roads are often quite badly corrugated. Expect to be a little rattled!
There are 3 main rest camps - Twee Rivieren (at the main park entrance), Nossob and Mata Mata. Camping at Nossob and Mata Mata will fill up relatively quickly (particularly Nossob). You can leave booking Twee Rivieren a bit longer. It makes sense to book at least your 1st and last nts there as Kgalagadi is a looooong way from anywhere and distances between camps is quite far. If you have time - longer is good.
If you don't have a 4x4, I'd recommend spending the most time around the Mata Mata area (the Aoub River bed) where it is much easier to see in a small car. But definitely still go to the Nossob River side as well.
If possible - stay at all 3. And if possible - definintely try to stay at one/some of the wilderness camps. Urikaruus and Grootkolk would probably have the best game sightings. KielieKrankie is in a stunning location on top of the dunes. Book Urikaruus and Grootkolk 11+ months ahead (or keep an eye out for cancellations).
Check the SanParks forum (Arid Parks) www.sanparks.org/forums for excellent and detailed advice/info on the park and each of the camps.