I would perhaps expect shuttles to have greater ease of launching and landing on Earth. After about 10 successful runs I would say we can mark the start of private space exploration.
This is the beginning but nothing is certain at the moment. I wish SpaceX only success though, they are working on something great.
I personally wouldn't use any single event to mark the "start" of private space exploration. It's a gradual process, not something that happens all of a sudden.
If they succeed in evolving this to a higher level of sophistication and functionality people will point to this mission as the start of it all.
If they fail they will point at this mission as an example of a foolish pursuit that should have been left in the hands of government agencies.
Either way this is, without a doubt, the start of the private sector launching into space exploration. Nobody can point to any other private mission that launched a capsule, docked at the space station and then returned cargo to earth.
