I need to bore a 3" deep, 1-1/8" diameter hole in the direction of the wood grain in mahogany. There appears to be many drill bits options including: spade bits, auger bits, ship auger bits, forstner bits, and probably others I'm not aware of. Which of these types would you suggest to keep the hole straight (no drill wander along the 3" depth). Any particular features to look for? A drill press will be used and bore rate is not a concern. Thanks.