If you're looking for more of a flat or matte finish, you should apply a redwood stain with an oil base every year. It's a chore, but one that will keep your furniture in tip-top shape. For a rustic effect on the redwood furniture, the driftwood look is what you want - but you don't have to wait until the elements weather the furniture for you. Use the subtle art of illusion - and some bleach. A water sealer should then be applied to protect the surface from really weathering.
Care here requires sanding and varnishing once a year to prevent oxidizing, peeling and splintering.
Marine varnish is often recommended for beechwood. Oak is wonderful and seems to fit in anywhere, inside or out. For the outdoor version, sanding and varnishing are necessary once a year for the same oxidizing, peeling and splinter prevention as beechwood. If you want a weathered, silver look, that bleach combination mentioned above will work. Then follow it up with an application of teak oil.