Wood for stocks is carefully selected for the grain. Cheaper production ones generally just want a nice straight piece without knots or deformities, grain running the length of the stock
Fancier stocks are hand selected to get figure and change of grain into the stock, while maintaining strength and not setting up potential fracture lines at the stress points.
Shouldn't be terribly hard for a lever action to get a nice piece. Bolt actions are more complex.
There are books written on the subject.
Your best bet is probably to get the tree sawn into planks as large as you can get them, let it season or have it kiln dried if that's an option for you, then spend some time researching how to select a blank out of your board.
Obviously, this is for a riflestock, a pistol grip would be much less complicated.