The two gateways
Cape Town (CPT) is the better airport for a Cape-first trip. Smaller, calmer, and twenty minutes from the city centre. O R Tambo in Johannesburg (JNB) is the country's main international hub. More flights, more airlines, and the only sensible connection point for Kruger, the Panorama Route, and anywhere north or east.
Which to fly into
Fly into Cape Town if the Western Cape is your focus. Fly into Johannesburg if safari or KwaZulu-Natal comes first. Doing both is common and easy. Domestic flights are cheap, roughly R800 to R2,000 one-way on FlySafair or Lift, near-hourly on the Cape Town to Joburg corridor, and you should book the leg between Cape Town and a Kruger gateway (Nelspruit, Hoedspruit, or Skukuza) as soon as your international dates are firm.
Arriving at JNB
O R Tambo is modern and efficient. The one thing to get right: don't accept an airport-lobby taxi tout. Either pre-book a transfer through your hotel, take the Gautrain (the airport rail straight to Sandton and Pretoria, clean, safe, fast), or use a ride-hail app. Driving yourself out of Johannesburg at night is the one arrival we'd tell you not to make.
Arriving at CPT
Cape Town International is small and quick through. A MyCiTi bus runs the airport-to-city corridor cheaply; a metered taxi or Uber is twenty to thirty minutes and R200 to R350. Car rental desks sit in the parkade opposite the terminal.
Domestic connections worth knowing
FlySafair, Lift, and Airlink are the reliable domestic carriers. Avoid booking a same-day arrival straight into Kruger. Give yourself an overnight at a gateway town, Nelspruit, Hazyview, or Hoedspruit, if you're flying in late, so you don't enter the park tired and in the dark.
The open-jaw trick
Most two-week visitors should fly into one gateway and out of the other. Into Cape Town, out of Johannesburg, or vice versa. It's usually the same price as a return and it saves a domestic flight and a wasted day. Ask for it as a multi-city ticket rather than two one-ways; the airline sites sometimes price it worse if you build it piece by piece.