"I've always thought that the best approach would be to float something up to the edge of the atmosphere then have a much smaller rocket blast to get it out into space."
You still need to reach "escape velocity" although having used say a large helium balloon to get to the brink of the atmosphere, you wouldn't in principle then need as big a rocket to go the final few km.
But you'd still have to accelerate much more quickly to reach the required velocity and that might put larger G forces on the payload.
Time might also be an issue as it will take longer for a balloon to "float" up to the required altitude and it will be dependant on wind speed too - as you wouldn't want it in the wrong place so it cannot achieve the correct orbit or geostationary position. Also, I guess the helium would be lost so that would be a cost issue?
Of course Virgin Galactic are still planning to use a larger "mothership" to fly a smaller passenger craft up to the edge of the atmos.