The best border treatment I have found for our yard is simply a 4" deep groove dug with a straight sod shovel. you then rake the soil or mulch etc. away from the grass to leave an edge of exposed grass roots. This gives you automatic air root pruning to prevent the grass from creeping into the play area. It just has to be refreshed each spring and/or spot treated as needed. And it's really easy on the pocket book, never needs to be replaced, can be adjusted to changes in your landscaping without any difficulty. I learned this from my neighbors, who are scary in their meticulous care of their yard. Trust me, if there was a better way to do it, they would. It really gives a very clean definition to different ares of the yard. Good luck.
Martha