The next step was to dado the edges where the sides and bottom met. I also used the dado blade to cut the front face so it to sat into the front not just on top of it. Once these cuts were made I glued and brad nailed the sides on.
I used what I had left of my stash of 18ga stainless steel brad nails. I've had them for years, and think I got them from McFeeley's, but I do remember them being quite pricey. If you fill the nail head holes with wood flour or glue & sawdust you should be fine with any brad nail, especially under veneer. I like the stainless brads so they never rust & bleed through in the moist marine environment.