Altitude as opposed to velocity...

In the old "Legion of Space" space opera series by Jack Williamson,
the spacecraft used a combination of rocket engines for landing and
takeoff, and 'geodyne' drives for long distance travel and FTL. The
geodynes _could_ be used for launch and landing, but were so powerful
that it was considered foolhardy and dangerous, so instead convention
reaction engines lifted the ships to a safe altitude and handled final
landing.

Anyway, in real-world space applications, velocity is the key goal
sought by rocket builders, rather than simple atltitude. But suppose
we had a drive that was like that in the old story, but had to be
started up and shut down at a given atltitude, so rockets are used for
launch and landing, but nobody cares about the velocity of the ship
when it reaches the magic altitude, the magic engine can make up that
difference, and can bring the ship down to whatever velocity is
convenient for turning on the landing rockets, too.

So, what I'm asking is how much smaller and easier it would from an
engineering POV to build rockets capable of just achieving a given
atltitude, if we don't care how fast the ship is moving when it
reaches that point? To make it more specific, say we built a vehicle
with the mass of the space shuttle orbiter, if all we cared about was
just altitude, how high could we get such a vehicle on built-in,
single-stage rockets if the velocity at maximum altitude is irrelevant?
.

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