Epoxy is the best choice. Remember surface preperation is more important than the bonding agent.
Wood, use good tac rag, but use 120 grit red garnet paper for a rough up, some wood fibers for the epoxy to grab. The wook should also be "dry" under 12% moisture contentant.
Metal, scuff also, no less than 120 grit Silicon Carbide (black) sand paper. Then use a no byproducts cleaner. Acitone use with appropriate safety steps.
Roll the adheared products, probably from the wood side, to remove as many bubbles as possible. You could use a vacuum chamber to remove all epoxy bubbles after mixing.
This set of steps should give you the best adhearance between dis-simular items, as you describe.