We've explained the difference between absolute and relative numerous times so you should have been able to make your own decision by now with a little thought.
In this case it doesn't matter because the parent element is already out of the flow with absolute positioning and the child only has one element in place so whatever you use will not affect anything else.
I would use absolute positioning in order to use auto margins to centre it horizontally and vertically without guessing at offsets needed.
z-index:-1;/* move it under the image*/
We've already explained stacking levels and z-indexes for positioned elements so you should know that raising or a lowering a z-index will move an element up and down in its current context. I've just used a negative z-index to move the play button behind the image.