Space is a big place; you shouldn't go off to random worlds to look for aliens. You should listen to what the people you already know have to tell you. Starbase commander Hayes for instance can tell you a bit about some alien species.
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“When Juffo-Wup is complete when at last there is no Void, no Non when the Creators return then we can finally rest.”
*dies of heart failure* CLEAR!! Ok, now that I see this, I have seen the light and must finally find out what the heck I must do in this game, I am almost good and cannot do anything right. must, print, map...
Well, the first thing you wanna do is make your ship badass, like max out your accelerators and thursters and that fun stuff. In terms of meeting new aliens though, Hayes(the starbase commander) is the one you want. Whenever some alien race tries to make contact, Hayes will inform you, telling you theres a signal from some direction. Furthermore, he has info about other races, like the old alliance, and diggin around those places is a good place to start as well.
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I like to think you killed a man. It's the romantic in me.