That's a pretty good description of an oil finish. No build, warm, close to the wood look and maintains the feel of the wood.
Danish oil would probably be your best bet. It contains some varnish resins which provides a little more protection then linseed or tung oil but not enough to really build unless you work very very hard at it, and that is a pretty pointless exercise.
If you haven't stained yet Watco Danish comes in natural and with color already in it.
Note, any natural oil will darken and slightly yellow when applied. Nothing to panic about but something you may want to keep in mind so it doesn't come as a surprise.
Good luck