You can fly to Nelspruit/Kruger/Mpumalanga (MQP) airport, which is basically the main airport serving the park, being just about 15kms away from one of the southern gates, best access for the larger southern parts of the park, flights by Airlink/SA Express (about 1hour from JNB (6 daily flights), 2h30 from CPT (1 daily) and 1h15 from DUR (2 daily).
From JNB you can also fly to Hoedspruit (HDS), which is a bit more to the middle gates of the park (1h10, 2 daily SA Express flights). Or to Phalaborwa (PHW) which is the airport most north, although still half-way up the park, 2/3 daily Airlink (J-41) flights.
If you want to drive around in the park, you won't be doing the whole park in a week, way too big. The southern parts has lots more tourists, traffic can get jammed on the roads even. The more north you go the quieter it gets...all the areas is good, some offer more animals of certain species in specific areas of the park.
Good luck and enjoy!