Well, it heavily depends on the starting velocities much more than the height. In fact it could be detrimental, because a craft higher up would have to accelerate harder to reach orbital velocity, than one lower down.
Personally I've always thought space plane using a multi-mode Jet/Air-augmented Rocket/Rocket powerplant and an Aerospike nozzle would be the best bet for an efficient launch platform. The Jet engines push the craft to say mach 1-2 relatively efficently (Jets can have a specific impulse in excess of 6000, while the best you can get out of a rocket is 250). As you gain height and speed the AAR takes over, getting about double the ISp of a rocket, with the rocket making the final boost.
This engine concept sounds much like the engine proposed for the HOTOL spaceplane proposal of the 1980's to me, although if you're using 1950's technology, could a extension of the powerplant proposal for the F-103 fighter have worked just as well...?
(The F-103 used a conventional Turbojet engine with afterburner. However the afterburner was designed in such a manner, that given enough speed & altitude, the turbojet could be set to idle, & the afterburner would then act as a ramjet taking the F-103 to Mach 3...).