Whether or not to stain depends on the wood you have and how you want it to look when finished.
If the wood is rather light coloured all around and you like it that way, don't stain it.
If it is somewhat darker walnut, you may like that with just the oil finish.
If you want it darker or a lot darker, then you need to stain it.
The only time I suggest stain right off the bat is when a stock has dark wood and some lighter coloured wood or sapwood in it. Then it is best to do at least the minimal staining to blend the stock into one homogeneous colour.
Oh, if you do stain it, I strongly suggest Fiebing's leather dye. If it gets too dark or splotchy, or any other problem; you can take off some, most or even all of it with alcohol or Acetone. I prefer to use their standard Medium Brown because it has a bit of red in it. I often mix it in a 1:1 ratio of alcohol or Acetone to get a lighter stain that I can "build up" the colour with additional coats to what I want. This is especially useful when you have a stock with varying amount of natural wood colour.
Oh, before you use this stain, I strongly recommend a thinned down coat of Birchwood Casey's Tru Oil be applied before the stain. And after you rub it in hard, wipe as much as you can off the surface before it dries. This will ensure you don't get blotches in the end grain of the stock. Allow that coat to dry overnight or all day if you can put it out in the sun. Then lightly sand with the finest grit sand paper you used, wipe or vacuum off the dust and begin applying the dye in light coats.
Gus