To drill pilot holes for wood screws, I hold the shank of a bit against the threaded portion of the screw and look at it against a good background. If you can see the shank between the threads it's too big. I like the pilot hole the same diameter as the center shaft of the screw so only the threads bite into the wood. To locate the center of the hole in the tang, use a brad point drill bit the exact size of the hole in the tang, put it in the tang hole and tap with a hammer. This will give you a centered punch mark to drill your pilot hole.
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Cody
BTW, always lubricate wood screws when putting them in for the first time. I use bear grease but something like linseed oil would work as well. If you don't you may twist of the screw in the wood.