I stored all my wood horizontally for many years, and I tried multiple ways to make it work for me. I never was happy with any of them as it always seemed that the boards I wanted were always on the bottom of the stack. I built a vertical rack about 3 years ago and I'm well pleased with how it has worked for me in my basement shop. It has 6 full-sized bays and 1 small bay separated by two rows of pipe and hardware from the BORG.
My basement shop is dry, but I still built a base to keep everything off the floor. You can see that the base is wider at the corner, which lets me store full-size sheets of plywood off the floor. The small bay is for large cardboard for stencils, the screen/storm doors for the shop, etc. I have almost 8-1/2 feet of height to the bottom of the joists, and a full 9+ feet between them. What you cannot see in the picture is that I have a small rack to the left that is attached to the joists that does allow me to store a handful of longer boards horizontally that won't fit in the vertical rack.
One thing that I would recommend adding to this style of rack that I have't yet done myself is adding some type of chain/cable/rope keeper to prevent boards from tipping out of the rack. I've never had that happen yet, but I suspect it is a matter of when it will happen, not if it will happen. If you do go with a horizontal rack, I'll second the recommendation that you don't need stickers if your wood is already dry.