I've flown JNB-LVI, which is a little longer than an hour. (Skatering has a good point about interlining.) But on visits to Swaziland and Lesotho I've only gone by road. I drove to Maseru myself, so I can't speak to the bus service there. I have taken a bus to Swaziland. It was the backpacker tourist Baz Bus, which is okay if you want to be taken between backpacker hostels and don't mind mixing solely with backpacker tourists. The Baz Bus is more expensive than normal intercity bus service but it's very convenient if you want to go directly between hostels. If not, there are better buses: Greyhound, Intercape, and Translux all run intercity coach services between major South African cities though you'll probably have to change to one of the local lines to get to Maseru and Mbabane as I don't think any of the main lines go to either anymore. (I could be wrong about that.)

Getting from Swaziland to Nelspruit some other backpackers arranged a private car and driver through the hostel and I got in on it. This is also a viable and relatively inexpensive option. In general, car is the easiest way to get around South Africa, and you can arrange a car and driver once you get there.

Finally, you can get nearly anywhere by minibus taxi, though I have a personal rule that I don't get in one for intercity travel for safety reasons. Within cities I've used them because traffic keeps speeds slow, but minibus taxi drivers are notorious for high speed driving when they have a long distance to go. Also they don't have much room because they leave when full.

Johannesburg has a bad reputation but I quite like it. The food's great and there's a lot to do there. Watch for theft, though. Park Station (Johannesburg's train and long-distance bus/coach hub) itself has a lot of security but wandering around outside (which isn't particularly necessary as most everything you need will be within) with bags is a good way to get something stolen. Getting from JNB to Park Station is easy as Gautrain connects the two. JNB has a bus/coach terminal also with shuttles to Swaziland operated by companies like Sky World Travel and TransMagnific. They go from the Sandton Gautrain station and stop at JNB on the way to Swaziland.

Best of luck and have a good trip.