I like to use a combination of BLO and/or a wiping varnish (usually Minwax Antique Oil Finish) and some finishing wax for maintenance. Having said that, I think the satin look can be achieved using just about any medium. If using a surface build-up type of finish (poly/varnish), it's about surface prep, making sure pores are filled and flattening the surface for a consistent evenness. If using a gloss finish then it just needs to be knocked down to satin with some 0000 steel wool.
If using a penetrating oil finish, its about good surface preparation to get the result. We each have our favorite finishes but I think it is more about the method that achieves the outcome...