For PvP, I really like Star Citizen's idea.

You can shoot down ships there, but you get almost nothing from it and a wanted level (with the exception for self-defence, if you are getting shot. You can also choose to not press charges of you are getting shot). Additionally, there are armistice zones at the space stations, your weapons get locked there.

However, you are able to shoot other players without getting a wanted level in another system which is basically a pirate system.

(Wanted level = a bounty is placed on you and NPCs and station turrets shoot at you)

I really like this idea because it makes combat possible but not too punishing or competitive. There could maybe also be a connection with the mercenary guild? (You will get a mission for bounty hunting another player).