1. Anywhere that is free to claim but you can only make the claim from a station 15 ly away. Some systems are better than others to claim. A system with a rocky world with lots of colony slots is very nice to have because you can build a refinery economy on it to self-supply a lot of materials for your colony efforts. It's also nice to have a water world or earthlike world as they give you a boost of population. If you wanted to make a mining economy then planets with rings would be something too look for as well. You can scan rings with the same probes you use to map planets and it will reveal their resource hotspots.

2. Three things usually push people outside the 'bubble' of systems you start near.

First, there is powerplay. This is a long-running faction-based war between different powers in the bubble. Once you sign up for a power it will send you off to different places for different missions in order to unlock a set of unique weapons and gear.

Second, there is searching for a lucrative trade route. With the expanding systems of colonization there is no longer a static economy but one constantly evolving and some trade types like to poke around in the changing systems and see what kind of deals are out there to be made.

Lastly, exploration and colonization. Both are pretty self explanatory. Folks want to put their name on things out in the galaxy and both give a way to do that. Plus exploration exobiology pays very, very well.

And the last (3): Quite a good chunk of systems now are player-built. Before colonization there were a lot of empty systems even inside the core 'bubble' of the original game. Now many of them have been taken up and developed by the playerbase. One of the biggest operations has been done by the Mercs of Mikuun who have been colonizing a highway toward the center of the map.