I am not sure precisely what you mean but I will take a stab it it.
I usually use a forstner bit for 1 in or more. And if it is a long piece like duck call or so, I drill in on the lathe. For plywood - I use a corded drill. For small pieces of ply or boards that will fit on a DP table - I use the DP.
The above scenario is when I want clean smooth cuts and sides.
IF smoothness and accuracy is not an issue, I use either spade bits or spiral bits.
If you mean 1 inch pen blanks for large pens, I use regular bits, but often do that on the lathe.