Have you found the SanParks forum? They also have tons of information about routes, what to take and how to get the most from self-driving.
You are right that you cannot do any of the walking activities from the main camps because you are not staying within the park. Since you haven't been on safari before and can only be in the park during daylight, consider going on an 'external sunset drive' or night drive from Crocodile Bridge. It gives you an opportunity to be driven around, ask questions of the guide and use spotlights to look for night-time animals. You need to pre-book.
Johan's advise is of course great. With such long and hot days in December, you may find you want to go for a siesta in the middle of the day, either back at your accommodation or at one of the many rest camps or stops where you can get out. Note that Skukuza has a day-use swimming pool (although it is quite a drive from Croc Bridge and back). Buy the map at the gate, but this one for example shows you lunch spots, hides and other places you are allowed out of the vehicle (e.g. Hippo Pools at Croc Bridge, viewpoints near Skukuza:
https://www.safari.com/kruger-nation...south-section/). Of course self-catering will be cheapest. We particularly like to have a thermos of tea/coffee for the mornings to stop at a dam or waterhole or view overlooking a river bed and just sit with the windows open listening to the birds and see what you see. But the picnic sights and main rest camps all offer very affordable food too. Most overlook riverbeds or are at high lookouts. Just get yourself a stick to wave at the baboons if you stop at Nkhulu.
My main advise is to drive really slowly (20 kph or less) with the windows down, don't expect to get very far in a day of driving, and stop at river crossings / bridges / culverts and have a good look with binos up and down the channel. Don't get too hung-up on where you are travelling 'to' because what you see crossing the road will mostly be luck with being at the right place at the right time.
Enjoy.