Initially I'm expecting moderate mayhem, station areas are most likely to be safe, but outside of that there's always going to be someone who wants to try their luck as a pirate. After a few weeks, when things bed down and people learn the local geography (or cosmology, whatever

) we'll have a larger version of what we're seeing in Alpha at present.
Some areas will be clearly no-mans land, others will have attraction for both the more passive players to make money, but also attract those that will prey upon them and relatively safe areas/routes that will mostly be peaceful but still punctuated with the odd, unexpected attack.
The beauty is, because the galaxy is vast and dynamic, no single area should remain politically static. Inhabited, explored space isn't confined to a few localised systems, so differing dynamics are going to develop across the known galaxy. I do wonder if eventually we'll see the player-population equivalent of
Heat Death, where the explored territory becomes so vast that even a large player base ends up spread very thinly, at which point our encounters are more likely to be defined by the game's mechanisms (NPCs) than by player intervention.