I'm sure a Golem could wear armor or use weapons, even magic ones (caryathid columns do), though I would force the character to find large or huge equipment for golems larger than flesh golems, and not allow stuff that could be used by a typical character (like the boots your half orc barbarian sells to the gnome fighter).
I would not allow them to use wondrous items as I would reason that their incredible magic immunity would prevent passive use items (like boots of elvenkind), or their intellect would preclude the ability to use commands (like boots of teleportation).
I would not allow them to use wondrous items as I would reason that their incredible magic immunity would prevent passive use items (like boots of elvenkind), or their intellect would preclude the ability to use commands (like boots of teleportation).