Well remember physics constrains everything, so it's interesting to look at that too. The reason we'll look into expanding in the first place is because of energy/material constraints in our own system. Some systems will require large "seeds" to boot up depending on how advanced we are at a particular point and how long can we wait for booting. Then as soon as it boots it will start receiving updates on how to improve itself, otherwise it would be terribly outdated by the time it starts exporting computing. What we choose to colonize will probably depend on the specifics of the system, like solar power output, material availability at planets, etc. There's a question on what kind of information the seeds will produce too: improving themselves should be largely redundant with the improvements made by the colonizers, which would be streamed to the new planets. So they'll be some very long term tasks so it can be efficiently divided across the decade-or-more latency separated systems.

I need to write a book about this some day. It's just so fun to imagine :)

It might not be practical to send information as light. You'd need a powerful transmitter so your signal can be detected among the noise from stars. It might turn out that sending a spaceship is actually cheaper and just about as fast. The spaceship can steer itself and doesn't spread out the further it goes.

I think galactic civilization will either solve noise problem or install enough repeaters if that's cheaper. Repeater network will have enormous fixed cost, but I don't think its variable cost will be higher than spaceships.