Actually, you don't need to orbit to go that high.
In the coming years, there will be suborbital flights capable of going as high as nearly 500km (over 300mi). You only need a good 5,000kph sounding boost to reach those altitudes. You don't need to reach anywhere near escape velocity (5x as fast, depending on altitude for various low earth orbit, LEO heights).
For safety reasons, however, it's very unlikely there will be commercial, sub-orbital flights that won't go higher than 150km (under 100mi). You'll earn your space wings for going higher than 100km, but it's very unlikely they'll go anywhere near 500km for safety reasons.
Manned space flight sticks to the bottom of low earth orbit (LEO) to no more than 200-250km typical. Satellites are typically twice that high or more and not in the same space. Then most go out to various altitudes, before geostationary at 36,000km. Anything beyond that is non-Earth and you start talking about solar orbits, etc... Geostationary is where the resulting linear sweep of the earth's rotation at an altitude equals the same velocity required to reach that attitude (perpendicular to gravity and in equilibrium with/against gravity's pull). It's much easier drawn and explained visually. Simply put, you're going fast enough (at the appropriate vector) that if you look down at a friend on the Earth, you're in the always same position above them (at least at the equator), as gravity pulls you back "around" the Earth -- in sync with rotation.
This mission was to Hubble, so they are at a much, much higher orbit, as well as more polar. Polar shots from the pad scare the **** out of most people because they don't understand why the Shuttle rolls and then banks at such a steep angle. As I mentioned awhile back, at one launch back in high school, one girl thought it was going to crash. "Doesn't it just go straight up into space?" Um, duh, no, sorry, pay more attention in class please.
