Well, a whole lot of that begins with the piece of wood you're working with. That incredible piece of shotgun stock there in the second picture was probably worth over a grand before anyone carved it to final shape and put that finish on it.
Making the very best out of figured wood is part art and part science, but what you DON'T want to EVER do is grab some Minwax or other can of stain and slather that onto your raw wood. You'll end up with a muddy, blotchy, disappointing mess that from the sounds of your comments, is probably something you've already experienced.
You have to be very careful and conservative with any finish you use that has pigments in it. Pretty much any stain. If you hit raw wood with that, the pigments concentrate in some parts of the wood and don't penetrate others very well and instead of a nice even color, you've got something that looks home-made. Blotchy and muddy and dull. That doesn't matter much when it's a laminated AK stock, but a fine walnut rifle or shotgun stock deserves better. You want the shimmer and fire and depth of that figure to "pop," not be slaughtered by a slush of pigments.
A very safe choice is to use a natural oil finish. There are lots to choose from. I like Watco "Danish" oil finish. Birchwood Casey's Tru-Oil is popular. Those are both actually oils blended with varnishes. The even more traditional choice is simple linseed oil. The more coats you apply and the more rubbing you do, the smoother and glossier the finish will come out. Natural oil finishes are easy, just about foolproof, and look terrific.
If you really need to stain the wood to get a different color tone, you should pre-treat it first to keep that "grain delta" problem from developing (i.e.: that "Unfinished Furniture Warehouse" home-made look
) but that's where the art and science get tricky. If at all possible, get a piece of the same type of wood you'll be working on, and practice a few trial runs to see how much of what makes the result you want.
Another possibility that's become popular in recent years is to use an analine dye before a top coat. I've not got much experience with those, but the results can be anything from mild to wild. A little googling should give you more advice there.