You have to use actual TREATED wood, not the stuff they paint on it or dip it in, but actual PRESSURE treated Lumber. You will know the difference by the marks it leaves on the lumber. None of this wood should be exposed to standing water. That means it shouldn't sit IN the gravel, or dirt, or anything else. Treat it like a ground level deck. Posts sunk into concrete, beams on the posts, and your cross boards sitting on the beams. Kind of like an inverted rail road track.
The boardwalk will be more interesting, and harder to build if you can introduce a meandering curve to it. To accomplish this, you will need to reduce the width of the inside of each board on the curve, by tapering the sides from the outside end to the inside end. That way, the gaps between the boards remain consistent.
You can also deck the boardwalk with 5/8" cedar decking, but I prefer to support it 12" oc to prevent warping and deflection. Use screws to put the decking down.
gravel beneath the deck is a good idea, along with some filter fabric or 6 mil plastic. This will slow down the growth of weeds and grass beneath the walk. (Nature is very persistent)