Yep, what Kitkun said. The research icon looks like a warp trail sort of thing heading towards a distant star, should be the same for all races (amazing the little things you stop paying attention to after a while). After you research it, just right click on the other star/planet/whatever. Your ships will go to their system's star and from there jump to the other star - it's always star<>star travel. All stars are also automatically connected, so you can go from a star to any other star on the map, unlike a normal phase lane.
As for the realistic maps, the game comes with an in-game map generator that you can set to create whatever map type you like. You can easily make 50 stars with ~10 planets each, and have direct control over how many are habitable, and fun things like that Feel free to play around it!