So here's the deal. Going to orbit is an energy game, not an altitude game. That's why there's such a huge difference between (as pointed out) New Shepard and Falcon 9/Dragon. Both carry roughly the same number of people, but F9 is an order of magnitude bigger. So let's run the complete numbers, shall we?
This is physics class, so we're going to assume that the Earth is a non-rotating, atmosphereless sphere. Not perfect, but it puts a lower bound on how much energy it takes to perform a particular launch. If I were to send an object straight up with the intention of getting exactly to the Karman Line and falling straight back down, I would need roughly 1 kJ of energy per kg of mass to send it on such a ballistic trajectory.
On the other hand, if I were to do a Hohmann transfer from the Earth's surface to a 100 km circular orbit, I would need 31.5 kJ of energy per kg of mass at launch, plus another 0.25 kJ/kg after coasting to apogee. All of this energy comes from the fact that I need to kick the vehicle sideways at nearly 8 km/s (17,900 MPH) at launch to get where I want to go as opposed to only 1.4 km/s straight up to hit the Karman line. And yes, you read that right, you need 32 times the energy to reach orbit that you need to reach space.
There have been proposals to use air breathing (read: jet engine) powered aircraft to get stuff part of the way to space, then use a rocket to finish it. The challenge to this approach is that the key as shown above is not altitude but speed. Such a jet powered first stage would need to reach speeds in excess of Mach 5-10 (roughly 1.4-2.8 km/s at altitude) to be even remotely worth the extra complexity. This is well within the realm of scramjet propulsion, which is in its infancy. Current air launched space launch vehicles (e.g. Pegasus, LauncherOne) get a small performance margin over their ground launched brethren, but the primary advantage is launch site flexibility and relative immunity to weather related delays.
I also wanted to comment about Methane-fueled rockets. Someone pointed out the high cost of refined kerosene as rocket fuel (RP-1/RG-1) because it needs to be very tightly controlled over just using kerosene out of a pump at your local gas station. Unfortunately, this is also true of rocket-grade methane. Early proponents wanted to use LNG straight from the industrial supply and ran into the same problems as did early kerosene rockets. LNG contains, among other things, a not-insignificant amount of ethylene, acetylene, sulfur, and sulfurous compounds. These cause just the same problems for rocket engines as do low-grade kerosenes; i.e. fouling of cooling channels and injectors leading to hot-spots and engine failure. Starship, Vulcan, and New Glenn need/will need to use highly refined Methane and not LNG to avoid these problems. Whether rocket-grade methane will be any cheaper than rocket-grade kerosene remains to be seen. Also, methane does have the disadvantage of being less dense than kerosene, so your stages need to be larger to hold an equivalent mass of fuel, which is what really matters int he rocket equation. See Vulcan stage 1 versus Atlas V stage 1. (Having said that, I am all for methane/LOX engine development for the eventual Mars in-situ fuel generation reasons.)
One last thought: there is a completely green rocket propellant: hydrogen. But that is a whole other logistical can of worms that I'm not going to open.
TL;DR: space is difficult.