The article on SpinLaunch--spinup to orbit--referenced Project HARP, which I'd forgotten about. Gerald Bull's idea was to send solid stuff to orbit with a cannon loaded with a rocket. You need the rocket to change the direction of your satellite once you get high enough and maybe get some extra speed as well--otherwise your orbit will intersect the Earth again. It could have worked, though the design would have needed some changes to get different orbit directions. Made of two 16 inch battleship guns, one version sits in Arizona and another in Barbados. They're impressive bits of hardware, though the Barbados one is pretty rusty.
SuperHARP is still active. It uses hydrogen/oxygen for the propellent (with some helium in there too) in a 2-stage push. For the same energy, the hydrogen and helium get higher speeds, which helps getting the maximum speed out of your projectile. They claim greater than Mach 32 for the record so far. "Green Launch estimates the acceleration forces involved will peak at around 30,000 G, and it's got a simple enough test for whether a piece of electronics can withstand that sort of shunt: sticking the component to a golf ball with epoxy and whacking it with a three wood."
SpinLaunch sounds interesting too, though it has its own problems--the jolt the bearing will take when the rocket is released, for example.
I'd bet there's some advantage to launching from a nice tall mountain--less atmosphere to go through.