If you have a friend who is a serious woodworker, try to get him to lend you his Forstner bits.
These bits have a razor sharp rim which allows them to cut straight even if the edge of the bit is partially over a void (like overlapping holes to reduce weight!) and regardless of how the grain twists and turns. You can also start them on even a severe angle, and they will continue to go straight.
They are a joy to use (the so-called "sawtooth Forstner bits" act mostly the same, but the edges of the holes are rough & ragged, not polished and smooth like real Forstner bits). This won't matter inside a buttstock of course.
Here is a picture of a good set at
www.leevalley.com :
These bits have to be used with a drill press, and they are rather expensive.
However, they were designed to make overlapping holes (to make mortise joints) -- you won't go back to spade bits, twist drills, or even brad-point twist drills after you have used one.
You may need an extension to go full depth on a buttstock.
John (woodworker/cabinet maker on the side...