Saturn V was a 'multi-gear' rocket. To lift off the pad, all 5 main rockets fired. As altitude increased, the center rocket turned off to minimize stress on the rocket (stay subsonic???)
Space shuttle also has multiple speeds. If you remember the Challenger disaster - the last message from ground was "Go with throttle up" Apparently the shuttle was high enough to go full throttle (again) and not worry about aerodynamic stresses.
Most liquid fueled rockets are throttleable. Both the space shuttle and Saturn V's throttle down to avoid putting "too much stress" on the airframe. What this really means, is that they didn't want to put more weight into airframe structure, and instead reduce throttle to the point where the atmosphere thins enough that one can throttle up without surpassing the design strength of the airframe. By the way, this point is called Max-Q and for the space shuttle, it is at 11km in altitude. For the space shuttle main engines, this means they throttle up to 104% of specification power (due to improvements over the years, the SSME maximum safe throttle is actually 109% of specification).
One of the issues with the shuttles solid rocket boosters - they are steerable - allowing insertion into a very precise orbit.
Compare that with the typical home built - solid rocket, that basically goes were you point it...usually...give or take a bit.
The problem with solid rocket motors for space travel is two fold. The first is that they cannot be throttled or turned off. The second is that they are considerably less efficient pound-for-pound than liquid fueled rockets. The typical measure of rocket efficiency is specific impulse, which is measured in seconds. For example, the solid rocket boosters of the shuttle have a specific impulse of 242 seconds, while the space shuttle main engines produce a specific impulse of 363.