Oil. (or varnish)
Rub down first to remove surface grime
Tung - aka China Wood Oil - most durable oil finish - shrugs off water & resists heat & alcohol. 24hrs drying time and needs 5 or 6 coats - needs careful rubbing down with very fine silicon carbide paper.
Danish - Tung with dryers incorporated - tends to leave a gloss on the surface
Teak - Tung with dryers incorporated - tends to soak in and leave a satin finish - may need regular re-application
My preference for garden furniture but dirt will build up on the surface over time and require annual sanding down.
Alternatively - rub down and clean - couple of coats of teak oil - allow to dry for a week or so - apply three coats of exterior grade gloss varnish rubbing down and cleaning off dust 24 hrs after each coat - finish with a final coat of exterior matt varnish. Use good quality brush and check internal corners for runs as you go.
Varnish panels first - then interior uprights - then horizontals and lastly outside uprights.
Peccavi
August 2009