The PO used lemon oil and we continued with it. We apply it typically twice a year after giving the woodwork a quick wipe down. It looks great and couldn't be easier to maintain. I don't know what kind of wood it is, but it isn't teak. Last year my wife switched to a brand that includes beeswax (see link) and it seems more robust and long-lasting.

As Jeff said, don't do this if you think you'll eventually want to varnish it. My attitude is, go with what needs the least maintenance. It doesn't get much simpler than lemon oil.