I would remove everything that can be removed and take it home for refinishing. That said, for me, it would depend on how easily removed. I like exposed screw heads for easier maintenance. I would have to be exceptionally motivated to remove anything with screws hidden by bungs. It seems like a lot of work to sand off varnish to bare wood. Personally, I would avoid that by prepping for varnish recoat. Long term, I agree that oil would probably be the more satisfying finish. It's really a personal decision based on too many variables to generalize. It sounds like you are talking primarily about exterior brightwork. Most of the folks in our marina typically are busy with these tasks in the late spring with boat in the water, before the temps get too hot. I've seen mostly varnish and/of cetol. I don't notice any favoring oil. Obviously, the dryer the weather the better, but I don't notice anybody getting awfully concerned about doing the work in the spring when we have unsettled weather.