So, which writer best portrays something completely made up? Bit hard to say isn't it? If you want 'realism' then it has to be sub-c, so then I would say Clarke in The Songs of Distant Earth.
Now I think of it (neurons moving very slowly), Murray Leinster's Med Service tales seemed to try to make sense of space travel technology. They were enjoyable, one way or another.
Murray Leinster Series
I seem to recall quasi-realistic space travel technology in Journey to the Mushroom Planet. I haven't read the series in awhile, but I remember a character being stuck in a time loop after trying to leave the planet. Interesting stuff.
I'm going to assume that "Classic" is loosely defined. If so, I'd add Alastair Reynolds' space operas. His insistence on slower than light speed travel adds some interesting astrophysics wrinkles into his tales.
If you take House of Suns for example he has a group of itinerant people travelling the galaxy. They can't go faster than the speed of light (though Reynolds does even address FTL in an interesting manner in this book) but they do travel at relativistic speeds. Consequently this group might travel for a decade of their subjective time whilst centuries pass for the rest of the world. In this way these itinerant folk get to see civilisations rise and fall. Excellent book!Could you elaborate? Thanks.
Niven doesn't dwell on the space travel too much, but the Lying ******* is an interesting ship. I think the Man-Kzin Wars goes into the mechanics of space travel in the Known Universe more deeply, however, that was mainly other authors and not Niven.Ringworld by Larry Niven