I did the same thing with the dead space at the end of the tub in my other house. I used melamine shelving and haven't had any issues in the 15 years it's been in place.

If rest of cabinetry in house in wood I'd do wood. It would take an awful lot for moisture to ruin it. You can also do melamine interiors with wood doors that match rest of house.

I'd add that 8-10 inches deep is awfully shallow for linens.

I think the melamine will be fine. If it were me, I'd glue a cosmetic wood strip to the front edge, or iron on some white veneer tape.

The place wont be very humid for very long if you have an exhaust fan in the bathroom. In my bathroom I have never had a fogged mirror while showering and the fan was running.