The shuttle was a technological wonder. It was also a failure in that it was neither safe, reliable nor economical. The cost of refurbishing the shuttle between launches exceeded the cost of replacing a comparable non-reusable rocket. Most of this was not realized until it began service, and NASA refused to face their mistakes for decades. They were too happy shooting people into space for no good reason.
The X-33 project was doomed from the start. "Most technologically challenging" is simply another way to say "least likely to work." In any case, a single stage to orbit is neither economically nor technologically effective.
The essential problem is that since the fuel makes up over 90% of the total mass of the vehicle (at launch), the minimum thrust needed to get off the ground would produce at least a 10G acceleration before orbit is achieved, putting an excessive strain on the payload. Instead one must reduce the thrust by either shutting engines off, throttling down or using multiple stages.
Space-X has demonstrated a reusable first stage and orbiter, both of which have proven effectiveness. Other reusable orbiters are in development elsewhere.
However, much work remains to be done in improving second stage design. Since most of the delta-V for LEO is provided by the second stage, efficiency (specific impulse) is more important here than the first stage.
One idea worth exploring is the use of a MHD motor/generator in the rocket nozzle. As a generator, it could be used to power the turbo-pumps. All other power sources tend to be heavier, less efficient or have reliability problems.
As a motor, it could reach higher exhaust velocities than a normal expansion bell. It should be noted that once exhaust gases reach the speed of sound, they can no longer sense the low pressure beyond the mouth. They can however sense lower pressures due to widening the passage, hence expansion bells. The efficiency of an expansion bell in vacuum is determined by the increase in area from throat to mouth. Needless to say, there is a limit on how large one can make an expansion bell.
An MHD motor would accelerate the exhaust gasses directly, and as they speed up they will expand, even with a constant area and supersonic velocities. The difference between a DC MHD generator and motor is simply a matter of voltage and exhaust speed, and the difference between an induction motor and generator is a matter of phase velocity and exhaust speed. So it can act like a motor to get the gases up to speed, then act as a generator with (nearly) the same velocity profile.
Second stages usually stop just short of orbital velocity, re-entering the atmosphere over the Indian Ocean. During re-entry, the kinetic energy must be dissipated by heating the surrounding air. The highest temperature occurs at the beginning when velocities are highest and the air is still very thin. The greatest heating occurs deeper in the atmosphere. For the shuttle, this occurred about Mach 5.
The goal therefore is to lose as much velocity as possible as high as possible. Capsules expose a large blunt surface to slow down quickly. The shuttle used lift from its wings to stay high for a longer period of time. The problem is that every kG used to protect the second stage is one less kG of payload (or about 100 kG of extra propellent).
One idea worth exploring would be to use a large balloon. First, one would need to find an air-tight material which can survive the high temperatures. It would need to be inflated while still in vacuum, with additional gases added as the atmospheric pressure increases. It should also provide enough lift (helium or hot air) to land slowly. Finally, it needs to slow down the second stage rapidly enough so that the stage requires little or no thermal protection.
The only reasonable location for the payload is on the nose of the second stage. (The Soviet Buran design made no sense whatsoever, except to look like the shuttle.) The only problem is that this makes heat shielding the second stage much more difficult.
It should be noted that the tradeoff between a winged re-entry vehicle and a blunt capsule depends on the size and weight of the vehicle. There is a temptation to combine the second stage and payload into one winged vehicle, but this means dragging around the second stage engine and empty fuel tanks during orbital maneuvers and makes crew escape (for manned missions) more difficult.