Once you have prepared the wood surface by sanding, I prefer to apply the finish of choice by thoroughly rubbing it into wood in very thin coats with my finger tips. Avoid using cloth as it is subject to leaving lint in the finish. This is a rather slow process and requires allowing each coat to dry overnight. Buff lightly with 4-0 steel wool and thoroughly remove all traces of dust before applying the next coat with the finger tips in the same manner as before. I prefer using a finish that has a urethane varnish base. Minwax clear satin Wipe On Poly is my current favorite. I use it straight from the can. I have used other finishes such as Birchwood Casey's Tru Oil stock finish, Linspeed and one or two others. All will give you a great durable finish. I do not like any of the oil finishes such as Boiled Linseed Oil. It takes literally months to cure and it is likely to be rather sticky while it cures. This stickiness gets worse if you get the stock wet from rain, snow, perspiration, etc. My recommendation is to avoid using it and use one of the urethane based finishes. You can get the same look but it will be far more durable.
Using the urethane finish may result in a more shiny finish than you want. If so, once it has thoroughly cured (maybe a few weeks to a month), you can use a material called rotten stone mixed in either oil or water to gently rub out the finish to a soft satin sheen. If you can't find rotten stone in any reasonable size, look for Birchwood Casey's Stock Sheen in any sporting goods store that sells guns. It, too, will give you a beautiful soft sheen to an otherwise too shiny (to your eye) finish.
Use a urethane based finish. Apply with your finger tips, apply nice even and very thin coats. Apply a total of at least 5 coats. 5 will usually get it done on a hard maple stock but10 or more coats is not uncommon on an open grain wood such as Walnut. You will be very happy with the results.