The density of your infill (15% in your case) determines how close the infill pattern lines are.  The closer those lines are, the easier it is for your printer to span across them when it starts to build the top layers.

There are other settings that can help with that too.  You can increase the number of top layers to insure that the final top layer is nice and smooth without sags and holes.  You can also combine infill, and try checking the "infill only where needed".  The idea of this last option is that Slic3r will only generate infill in areas needed to support the top layers (ceilings).  Unfortunately it doesn't always work as you expect it, but try it anyway.

Just try different settings, the slice the object, then look at it in Repetier a layer at the time.  Pay particular attention to the few layers just before the first top layers.  Make sure they are in the right places.  If everything looks OK, hit print.

I printed at a 15% infill and that made it plenty sturdy, but I am wondering if there is a way to print it that would be more efficient with the use of filament.

I am not entirely sure what the support material function of slicer is. I had assumed it would add necessary support under structural portions of an object, but when I attempted to print at zero infill it didn't add anything and just had the printer extrude into "thin air."

I was hoping if I could get some insight on this object I would gain a better grasp of the overall process.

This is just a stand to hold some small one ounce bottles with each row stair stepped so I can read all of the labels without moving any of the bottles.