Indeed, Mastercard South Africa even has an ATM search to show you where the best ATMs would be that support it.
How much cash? That depends on how much you're planning to spend. Or are willing to keep on you at all times. Depending on which study you read, Johannesburg (I assume one of the cities you're visiting) is the crime capital of the world. I personally tried not to keep too much cash on me.
Yes, don't bring traveller's cheques. They're a pain, nobody likes cashing them any more, and some places may even refuse. Of course, if you really wanted to, keep some as a backup in case of emergency. The one big benefit is that they're insured - if they're stolen you can get the cash back, whereas if you get mugged and cash is stolen; tough.
Most places accept credit cards - VISA and Mastercard. Most restaurants, gas stations for sure. Little corner stores and street vendors - not so much. It helps to have some cash on you for those purchases, which you can withdraw from an ATM.
To be fair I was there in 2005 for a month, and 2008 for 2 weeks. In 2005 the only time we had a problem with a card being 'accepted' was when we popped up to Zambia, and they used the old-school swipe + carbon copy of your card technique.
There's been seven years since then, so many more merchants have upgraded, and especially after the 2010 World Cup, it's definitely a tourist friendly country (in terms of transactions, at least).