Yeah unfortunately the altitude isn't really the problem. It's high speeds that you want. The altitude just gets you away from the atmosphere which will stop you achieving the high speeds.
Maybe since fuel isn't so expensive it isn't such an issue anymore, but I really like the idea of somehow powering a vehicle with solar power. The nice thing about velocity is that without friction, you can get really fast over time even with relatively weak acceleration. No idea whatsoever how to accelerate a rocket with electricity alone, though... Is it even possible? I think NASA has some models, but for long distance stuff...
Lookup "Ion Drive". If you end up on a Star Wars site, you've missed; there's a real such thing that has flown in real space.
You can't launch on an Ion drive, though. (Even if you made it powerful enough, that would mean irradiating the entire launch area with instantly-lethal radiation, not a terribly social thing to do.) The way to a solar-powered launch is that you use solar power to create the rocket fuel, which in the simplest case is simply cracking water into H and O.
Solar panels are orders of magnitude away from being able to launch themselves in real time. Take a solar panel, compute its mass, compute how much energy it can generate in a day, convert that to potential energy in Earth's gravitational field, and you'll get a sense of the maximum speed a panel could possibly rise with perfect conversion of energy to height (which we have no idea how to do anyhow). I haven't done the math but if you get a rise rate of more than a few inches a second during the brightest part of the day I'd be surprised.
