The shuttle is a bad baseline for making an SSTO. it's a high density blunt body with the flying capability of a slightly rounded brick. Vertical may have advantages for getting to altitude quickly with a vehicle that is never going to land, but once you want a reusable runway lander you are already adding wings and wheels. not using them to allow a lower T/W ratio at takeoff is wasteful in that case since engine mass is a major mass contributor to the vehicle as a whole.
you either go vertical all the way, or you go horizontal all the way. both can have unpowered soft landings, and both share approximately the same vehicle mass per unit mass payload despite having wildly different trajectories. what you add in mass with wheels and wings you mostly get back with needing much smaller engines due to not having to support the initial take off mass of the vehicle on thrust alone. Sloping ascent is also a necessity for air-breathing propulsive stages.
What really closes the case for wanting horizontal launch tho is the flexibility of being able to use a flexible multipurpose runway to launch your vehicle instead of a specialized launch gantry. There are huge cost savings in sharing infrastructure between different users with differing, but still similar needs. the runway can easily double as a runway for normal air traffic when not in use by skylons.
The skylon spaceport is basically just an airport with added LH2/LOX refueling capability and a strengthened runway for skylon takeoff's. the skylon can land on any old runway on the way home since the vehicle itself is indeed light enough to not need especially strengthened runways on landing. it has burnt off all it's fuel after all.
There are good reasons for not wanting to go vertical on airliners, and almost all of them has to do with the economics of flight and ground handling to do. it's just so incredibly much easier to handle a vehicle that can be towed into the hangar for maintenance, and that can roll onto the takeoff field under it's own power during departure.
For an RLV to be economic it has to be capable of airliner like operations. otherwise it becomes just another rocket that needs a ton of supporting infrastructure and people in order to launch.