See our Visa requirements Section to get up to date information on visa requirements for South Africa, Zambia, Botswana, Namibia & Zimbabwe.
Never mind all the bad media, Zimbabwe is safe, be open minded this is Africa!
Victoria Falls is the center of the universe.
From South Africa you can fly from Johannesburg or Cape Town, Airlines that fly this route are Fastjet, Airlink, & SA Airlines as well as Air Zimbabwe to Bulawayo and Victoria Falls.
You can rent a car in South Africa and drive, see here more info on crossing borders in South Africa in a rental car.
From Botswana/Okavango Delta to Victoria Falls there are good local buses to Kasane/Chobe at the border.