What is a safe clearance for ground planes?
In your case the right answer can only truly be given by you and the person or people finally making the PCB. When I design with 5/5 track/clearance my pours often also become 5 or 8 clearance, because I know the fabs I use can do it at a price I am willing to pay and I know I will have taken care of larger gaps only where they are needed.

((I changed my wording to reflect what I think you mean. More usually planes are used to refer to the dedicated copper planes inside a multilayer PCB where no tracks run through them, where a pour is the copper areas you have on the signal layers of a given potential, such as a ground pour or VCC pour))

If you have no signals or pads that need to be further away from a ground pour for signal or thermal reasons or you know you have defined special rules for just those occasions, you can just set the general rule to 8 thou/mil as well. If you may have those signals and can't be sure everything takes that into account and on the other hand don't need to isolate your tracks from each other, you can keep it at 12, 15 or whatever.

Generally having ground between tracks can do little harm (unless the tracks it creeps between are characteristically coupled, like wired network, USB, RS485, etc) and often even improves things, especially if you do not have an actual ground plane on an internal layer.