If you want a perfectly realistic SF scenario, you could do well to use as a guide none other than one of the great visionaries of rocketry and astronautics, Konstantin Tsiolkovsky.
The Tsiolkovsky Plan Of Space Exploration (1926) was laid out as follows:
1) Creation of rocket airplanes with wings.
2) Progressively increasing the speed and altitude of these airplanes.
3) Production of real rockets-without wings.
4) Ability to land on the surface of the sea.
5) Reaching escape velocity (about 8 Km/second), and the first flight into Earth orbit.
6) Lengthening rocket flight times in space.
7) Experimental use of plants to make an artificial atmosphere in spacships.

Using pressurised space suits for activity outside of spaceships.
9) Making orbiting greenhouses for plants.
10) Constructing large orbital habitats around the Earth.
11) Using solar radiation to grow food, to heat space quarters, and for transport throughout the Solar System.
12) Colonisation of the asteroid belt.
13) Colonisation of the entire Solar System and beyond.
14) Acheivement of individual and social perfection.
15) Overcrowding of the Solar System and the colonisation of the Milky Way (the Galaxy).
16) The Sun begins to die and the people remaining in the Solar System's population go to other suns.
(
http://www.informatics.org/museum/tsiol.html )
You can outline an epic along the lines of the Tsiolkovsky plan, using as models technologies already on the drawing board or within theoretical possibility, and end up with a story of a space civilisation which endures for millions of years even after our own sun dies and humanity finally commences the mass exodus to greener pastures out in the galaxy. You could tell stories of people in spinning worldships in transit to another star system relatively nearby; how life in such an environment is altering human culture and the expectations of the population for what they'll find at their destination. You could have a thriving and populous solar civilisation consisting of settlements on the largest moons and stable planets in conjunction with very large space colonies located around each world and in independent orbits around the sun, and numbering in the hundreds or thousands. There is even room in this scenario for wars between the various solar nations and colonies which can be fought without recourse to FTL or other exotic technologies. You could have economies based upon harvesting hydrogen from the atmospheres of gas giants, metals from the asteroids and moons, and water ice from the comets in the Oort Cloud.
Such a background for a SF mass media series has already been executed in the form of the Japanese animated
Gundam franchise. The cast of characters are all human, and there is no FTL, teleportation, or contact with aliens. The setting is within the boundaries of the solar system and is much truer to the ideas of Tsiolkovsky than any other series.