This is a "what do you like" question. Choices are keeping it "natural" as it is, or coating it with cetol or varnish.
Some folks think varnish/coating is great and "nautical." I personally don't. I don't like the reflections down below off shiny varnish (I used to think it was nautical, but changed my mind

), and I use cetol only abovedecks.
We just use teak oil. I like the soft, un-shiny factory finish. Our companionway gets the most re-oiling, 'cuz as you've noted it gets the most sun. Others use lemon oil. I put the oil on with a wide foam brush and rub it in with a rag. Simple.
Your boat, your choice.