you can use laminate over melamine(I did before).
Pour contact cement on both side,use a fine roller then wait like atleast 20 min so both sides kinda dries then put em together.
yeah you should laminte the smooth side of plywood.for some weird reason,laminte sticks better with particle board or MDF.I laminated all ply,mdf,particle and best result was with mdf and particle.nothing wrong with ply wood,its just you gotta get the smooth furniture grade ply wood.if its cheapo ply wood then sand.
I say laminate both sides.you gonna build a panel then do it RIGHT !

(I would go for both sides).