There's no need to do faster than light, or even all that fast. The diameter of the Milky Way is at most 200k light years, with technology we could develop today we could populate the entirety of it with generation ships in the span of less than 100 million years, which isn't all that big in the scale of the universe.
I read this, and about ideas like the Von Neumann probe[0] all the time, and it really fills my head with concrete to try and reconcile those ideas with the fact that we haven't found any signs of extraterrestrial life yet. If it's so feasible in a "short" time relative to the age of the universe, where are all the probes?
That's exactly right, nuclear pulse propulsion is all you really need, and that was studied in the 60s with project Orion. The lack of probes is paradoxical i.e. Fermi's paradox (yuk yuk).
If you read about this all the time, then you're probably also familiar with the Fermi Paradox and the possible explanations for it. 2016 may have given us a clue as to which one of them seems most likely.
There is a star we've observed between 1400 and 1500 light years away with odd, non-cyclical light fluctuations. It may be indicative of a megastructure being built or falling apart around a star.
Unfortunately, I think a pulsar type situation is much more likely. There's many things that could potentially cause those fluctuations, especially considering our relative lack of knowledge about extrasolar space. In 1967 when we started detecting regular, precise bursts of EMR from deep space it looked a lot like aliens.
Software entities may experience reality a million times faster than we do now. Do you want to wait a quadrillion years to finish colonizing the galaxy? That is a really long time.
Also, if you okay more StarCraft, you won't be so relaxed about claiming unoccupied resources.