In fact, Atmo is very hostile for classical rockets. It makes them too sizable, heavy & inefficient as well. To shift this situation needs to get another propellant, but we have fallen short here. So, one of the available ways is to deal w/ air-breathing engines (turbojets or turbofans). Yes, very disadvantage gets to be low thrust-to-weight ratio == an air-breathing engine never beats the rocket ones.. Never. However, there is possible to use 2.5-staged design of rocket.
- rocket boosters to initiate sustainable aerodynamic lift: 100-150m/s.
- winged core with turbojet engine == it takes rocket up to 30km altitude & up to 800 m per second velocity (yes, for the most share of flight profiles, there will be more humble speeds & altitudes).
- upper stage, attached to the back of the core, makes the rest of its way to an orbit.
- core gets its way back to the runway.
rocket boosters & core stage run from the start, it's very reason why to call it 2.5-staged design (not 3-staged one).
Horizontal take-off is preferable to avoid gravity losses.
Design of wings is most tricky part in this scheme == one of possible solution looks to use partially dropping ones.