replying to Jdaley06, Iggy wrote:
Just about anything you'd expect will work solidly for decades. If flat backed,
Wood Glue...blue Titebond 2, very good tack or initial holding. For very rough
or uneven backsides go for much thicker caulk style adhesives like Loctite
PowerGrab, Silicone Caulk or even Latex Caulk. Do Not use "Construction
Adhesive", that LAUGHABLE GARBAGE barely lasts 10-years and should be outlawed.
You'll want to polyurethane (or 2-in-1, stain and finish) the entirety of every
piece so expansion and contraction doesn't happen, afterwards just glue them on.
If you like it a lot and might want to take it with you, then glue them to 1/4"
plywood and use a literal few screws to attach the panels to the island.