Traditional furniture finishes, like boiled linseed oil will give a nice satin sheen. Many thin coats applied will begin to build up. If you want more filled grain I have used pumice, ( spareingly) rubbed into the grain, along with the linseed oil. And if you want to build more on top of that, shellac is my favorite. Shellac will stick to anything, it is often used between dissimilar finishes as a barrier coat. I use a " traditional flake shellac" ( do not use the premixed stuff in a can) dissolved in denatured alcohol. You can control how thin, or thick you make it. Very simple to make and to use, very forgiving.
You could even alternate 1 coat linseed oil, 1 coat shellac. It would not take much to build a nice finish up on a wood that is as dense as you say. I have used these methods on many large pieces of furniture. Keep the coats thin to give the best water resistance. In the future you can give it a fresh coat of either and it willlook like new again. Try on some scrap first if you can. Ask any questions you might have.
Larry