Any Moses costume must include a robe. The simpler the robe the better, it should ideally be one solid color. It is known Moses wore a robe from Exodus 4 where God shows Moses how he will convince the Israelites God sent him by turning his hand leprous after he sticking it in his robe. The robe should also have a veil since the Bible says Moses wore one to cover his face once it began to glow upon coming down from Mt. Sinai (Exodus 34:35). The veil can be easily made from cheesecloth.
A proper Moses costume must also include sandals. When God first calls to Moses from the burning bush, God tells him to, "Remove the sandals from your feet for the place on which you stand is holy ground" (Exodus 3:5). While sandals in Biblical days were probably like flip-flops made from leather or leaves, any sandal you have laying around the house will work, especially since your feet will usually be obscured by your robes anyway.
Moses' rod, called the "Rod of God" in Exodus 4:20, is his most important item, his defining characteristic. In Exodus 4, God turns Moses' rod into a snake then back into a rod again as his first sign to convince the Israelites, and he later turns it into a snake again to convince Pharaoh. Moses' staff also heralds the coming of many of the plagues and is stretched out to split the Sea of Reeds. This rod should be simple. A large stick that can be used as a walking stick will do.
While the Bible never says Moses had a beard, a bearded Moses is so ingrained into popular consciousness that he will hardly be recognized without one. If the actor can't grow one naturally, inexpensive fake beards can be bought at party and costume shops, or one can even be made from yarn or cotton balls. The beard need not be white unless you are an aged Moses. Since Moses' face glowed post-Sinai, consider wearing very light colored make-up or even attaching a small LED light in the hood of the robe behind the veil.