Two things will be the most important on your trip.
Your car/van and your accommodation.
Go for a Volkswagen Kombi, or Mercedes micro bus.
Everyone is comfy with a high seat and a great view.
With 6 people you may consider hiring a 'VENTER' trailer.
It's small but you can plonk all the luggage bags in it and it frees up the van for more important things (camera's, cooler boxes, binoculars etc)
I saw this online http://www.sacarhire.co.za/pages/testimonials.php
, where they hired the car and the hire company provided the cooler boxes
(i have no affiliation to these people at all)
We normally take 2 cooler boxes for meats/chicken etc (3 or 4 people for 5 nights).
By the time you have put the food in it , with the ice, there's not much room.
You are going to need at least 2 cooler boxes for 6 people's food and maybe a smaller one with ice for cold drinks .
Depending on what time your flight arrives, I would consider staying first night at Skukuza (I am not a fan of Berg-en-dal).
Its a big camp, but the 6 bed cottages GC6D are very nice (quiet and away from everyone).
Maybe even 2 nights in skukuza, because packing and unpacking 6 people is a pain.
The family units in the park are two bedrooms, with three beds in each. (sleep 6).
Also, next to skukuza is the best waterhole in the park, lake panic.
Nice to break a game drive by chilling out there for an hour.
Getting food is easy.
You will be going through Nelspruit on the way there.
You will find everything you need there.
Think of it like this
Woolworths = Marks and Spencer
Pick and Pay = Waitrose
At pick and pay you could buy your ice boxes as well as a couple of storage boxes.
Ice boxes may be expensive R500 a shot, and the bins maybe R70 each.
You can pack all the bits (bread, tinned fuit etc in the bins).
Try and bring one of the fold up picnic cooler bags for your drinks.
I would avoid buying meats in the park (expensive and quality is not fantastic)
If you like chicken woolies (woolworths) make the best barbeque packs (kebabs come in sealed 6 units about 6 GBP per pack),
Fits easily into cooler, and its prepacked in plastic.
Get your cold meats (chicken, turkey etc and make sure its shrink wrapped.