I use stainless steel screws to fasten wood bits together. If you sink the head or place away from view the shine shouldn't bother you. I just use a bit of acrylic sheet on the bottom and bury that under the substrate, works fine. Slate or tile would be heavier and might hold it better.
Since your rocks are close to the same size you might consider studying up on iwagumi theory and place a couple rocks next to one another so they appear to be a single stone. Then the next largest would be placed to balance the largest and the last would balance the composition. The wood needs to be considered as well, no idea precisely just how it fits in but this article might help. http://www.thegreenmachineonline.com...s-introduction