In Cowboy Bebop, they had developed hyperspace gates that allowed ships to travel between the terraformed planets and moons in the solar system in a matter of hours. Gates are a frequently used method of travel, which helped in system defense. It may be necessary to use a gate to get to a system, but you don't necessarily come out of the gate, just somewhere along the edge and spend the next week or so transiting in-system.

For Firefly, basically they terraformed many of the planets of a binary star system. You get the impression that the core worlds are those intermost to their primaries, while the frontier were the outer worlds. Thus a trip between neighboring planets took days, not centuries.

I like Traveller's jump drives. C.J. Cherryh had something similar, but ship crews and passengers would not be conscious during their jumps. They'd hang saline bags for IVs and make sure water and ration bars were nearby for when they regained consciousness days later. Their biggest surprise was to find out one of the races, the Kif, did not become unconscious during a ship jump. Cargo was also packed in drums and loaded into a sort of giant rack in the hold.

Alternately, you could have some sort of unique warp drive. I read one where the warp field is generated by cables that retract into the hull following a jump to protect them.

For one of my games, I came up with an Exotic Matter drive - basically dark matter is like an iceberg - we see 10% of it at the normal space level, but 90% of the mass is "submerged" in a form of subspace. Exotic matter drives work by taking a fragment of dark matter at the heart of the drive and using fields to push the dark matter further into subspace, dragging the rest of the ship with it, partially submerging the ship into subspace in a sort of interface layer, so you're able to move at greater than light speeds while still able to see normal space.

But you have to watch out for gravity shoals, the wells created by the stars and even the dimples of planets. As you move towards a gravity shoal, the dark matter starts getting pushed back into normal space. The last thing you want to do is have a drive failure where the field collapses and the dark matter rebounds, swelling within the drive casing until it bursts through, splitting the ship apart. And then it returns to subspace, dragging nearby fragments back into subspace with it. 

I also developed a type 2 drive where additional coils allow the entire ship to be submerged in subspace and you navigate by detecting quasars as they pulse in both normal space and subspace. By finding the relative positions between two such quasars, you can navigate near enough to an edge of a planetary system, then spend the next two weeks going insystem to a planet, or if they have a way station, you travel to one of those to do your trades where someone takes your cargo to tran-ship to the planet, while you make arrangements to take on cargo shipment

However, not many have a type 2 drive.

Interstellar ansibles use the exotic matter drive to open a small portal into subspace so they can then transmit & receive, so you have near instant communications between systems. You could decide it still takes a week or more for the messages to be received. Also, ansibles are basically small space stations. Military ships can configure themselves to become ansibles, but they basically can't do much else while transmitting and waiting for a response.
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So no alien races yet. Are furries here basically chimaera? A mixing of human and animal dna?