I find I tend to put everything to Faster as I feel there isn't enough for me to do in-game to justify the lower speed settings. What settings tended to be used by the multiplayer scene?
Quitch
The tutorial tells you to order your fleet to phase jump to the nearby world, presumably the one with the question mark. You can use the move order or right-click. I right-click the world, my fleet phase jumps on over and a few enemy ships move into range... ...however the tutorial message never changes and neither my ships nor the enemy will fire on one another.
They found that the universe isn't infinite, and that it's imploding. They're heading towards the core to escape their inevitable doom, hoping to research a system which allows them to escape the bubble, which is why they have so much advanced travel tech.
Hopefully such a feature will exist at some point. Sword of the Stars had it and it was wonderful. No one around? Start up a multiplayer game with some AIs, and people just hop in and take over as and when. Awesome