My suggestion is to one. Use Nuclear power. 2. Use ramjets, scramjets, or a variation. 3. Do not obsess over single stagedness.
The solution I like the best consists of three parts:
1. Supersonic/Suborbital Transport. This vehicle is not solely for rocket launch, it is also a cargo vehicle. (Entering Space suggests market exists for four-hour intercontinental mail, and other markets). Used to piggy back launch from high speed and high altitude. If (sc)ramjets are practical , they should be used. This will provide about 1km/s dV at minimum (much more if ramjets or scramjets are used), plus whatever is wasted in getting off the ground. It can take off at an airport, and then go on to make its delivery and land on the other side of the world.
2: Universal Nuclear Space Shuttle: Powered by a DUMBO or NERVA variant rocket. Is lifting body re-entry vehicle, has dV of 7000-8000. This will be smaller than the STS orbiter. Therefore, it can launch into LEO from the back of the Supersonic/Suborbital Transport, be able to maneuver (which the Space Shuttle can barely do), and then land vertically. This would have no cargo bay, but it would have a flexible pressurized compartment able to take either several people (for space station service, etc) or a bunch of in-pressure cargo (replace the Progress, plus be able to recover equipment.) If delivered into orbit around another planet, it can have fuel for one landing and one takeoff. (Mars, Moon, or Titan under consideration).
3. Universal Nuclear Cargo Launcher: For launching large objects, but not for landing them. This consists of a very compact NERVA/DUMBO core, rocket engine, frame, ballistic heat sheild, and fuel tank with a fairing to go over the much larger payload. This is for launching sattelites. It is popped into suborbit, lifts into orbit, and then jettisons the payload, deorbits, reenters, and lands w/parachutes and/or airbags.