The original rockets blasted off with fires raging out their tails, much like the real thing. We all have images of cartoon and movie rockets from the 50's: basically missiles with some poor slobs strapped inside. Then came flying saucers. I don't know why the aliens always got the cool saucers and we had the exploding rockets. "The Day The Earth Stood Still" flying saucer barely impacted the crowd that gathered on the ground. SF during the early days of nuclear testing, called them 'nuclear powered'. Whatever that meant. I guess if it had nuclear power it could rise slowly into the air to the tinny strains of the theremin.
I think that the Jupiter II on Lost In Space was the first human flying saucer. It, too, ran on "nuclear" power so it just floated away on whimsy. Star Trek, way ahead of it's time on this, created the Enterprise, a ship that never landed and was powered by something completely unprecedented - crystals that held unimaginable power. They transferred this power to their engines, which had the capacity to accelerate them beyond the speed of light on a 'time warp factor'. A very nice gimmick to get them across great gaps in space in a short time.
This was followed up, a decade later by Star Wars and 'hyper drive'. These engines catapulted the ship across the galaxy in seconds by passing through hyperspace, which I suppose occupies a different dimension of space and is quicker to cross.
Since then, we've stuck with that basic concept for SF space travel. Hit the button, see you next Thursday. There are logistic problems but they're easy to gloss over because all we're trying to do is cover great distances in a hurry.
As an alternative, and we have to give Star Trek some more innovative credit, there is the personal transportation idea. Beam me up by transferring matter into coded energy and then reassembling it in its original form. This works better for short distances because the energy only travels at the speed of light. But there are gimmick ways around that, too. Ion propulsion, graviton waves, halcyon particles, the works.
A nod has to be given here Doug Adams "Hitchhiker's Guide" series and his improbability drive. Using the Heisenberg Principle, he fantastically imagined a mode of transportation that works on unlikely, and therefore necessary probabilities.
The big joke there is that modern physics experiments with particle transfer puts Adams ideas closer to the mark than any warp engine or hyper drive. The nifty thing that's going on right now is that a muon or lepton or some such teeny speck of a particle has been sent from New York to London by breaking it down and transporting it.
Here's the rub. What actually happened was that the original particle was broken down to the quantum level and then a new, identical particle was created in the destination location. You might think this is cloning. In a way it is. But the only way to succeed in this transfer was to destroy the original when it was sent. So you now have a clone but no original. The clone would be so identical that it might as well be the original.
Here's where the hand rubbing, speculative SF ideas get to come into the mix. New York to London sounds like going from Detroit to Flint. Who cares? But if we can extend the trip using the quantum principle where two identical particles can communicate across the galaxy instantaneously, then we got ourselves a quantum rapid transit system that requires no warp drive or stable worm holes.
Let's dehumanize this for a sec. Don't send people, send nano satellites that can gather data and send it back from, say, the core of our universe. Seriously, if the only data that reaches us from the center of the universe is 14 billion years old, wouldn't it be something to find out in a flash what's going on there right now? We could send quantum satellites all over the universe with one mission: signs of life. They could be designed to send signals back only if they are tampered with.
Scientists are already considering nano satellites launched from Earth, but transporting them on a quantum wave would be a cheapo way to explore the galaxy. We can work on how to shrink an astronaut into one later on.