Catch Wires
The launch loop will provide cheap, high speed vehicle launch into high apogee orbits, such as synchronous Construction Orbits. The vehicle can be passive, with a large orbiting station providing the delta V for orbit modification. Raising the vehicle's perigee above LEO will require some apogee delta V, ranging from 25 to 120 m/s.
These low delta V's can be provided with a cable arrest system on an orbiting station, resembling the tailhook capture system on an aircraft carrier. The same system can be used to launch a vehicle retrograde, slowing it down at apogee to reenter at perigee. However, this adds or subtracts momentum from the station, which must add (or subtract) thrust to maintain orbital position. This delta V can be provided with a very low specific impulse (ISP) rocket mounted on the orbiting station itself..
A low ISP is desirable for three reasons - it reduces temperatures, it permits a very cheap propellant, and it drops the enture exhaust plume into Earth's atmosphere, leaving no orbiting "molecular space debris" to impact other spacecraft. The propellant may be plain water electrically heated into steam, or mixed with some hydrogen peroxide (ISP 265 seconds). Given the limit on exhaust velocity, ISP will range from 145 seconds (one day construction orbit) down to 30 seconds (ten day construction orbit).
The energy for electrical heating can be generated by adding radial velocity to the incoming vehicle (launching slightly faster and earlier). The catch wires slowing the vehicle relative to the station can be spooled around drums driving electrical generators, providing power to the propellant heaters.
Some nice drawings here, Real Soon Now.
Incoming vehicles will be dumb and passive - they will have a small emergency rocket engine providing less than 2 m/s of delta V near apogee, dropping perigee from 80 km launch loop altitude to 50 km reentry altitude. Manned vehicles (and expensive cargo) will require heat shields and parachutes resembling the Apollo capsule; expendable cargo will be allowed to crumple and plunge into disposal areas over the ocean. My guess is that a destructive reentry won't "burn up", but will break up.
An alternative thrust system might be simple panels of laser-ablative rubber, with laser stations in orbit capable of pulse heating the surface of the material and throwing off a few grams of mass, creating a few newton-seconds of momentum. However, this is likely to leave plume debris in orbit.
However, for 99%+ of all vehicles, missions should be designed to operate passively, with almost no expended reaction mass. A spacefaring civilization will have billions of tonnes in Earth orbit, and zero tolerance for uncontrolled material and rocket plumes in those orbits.