A simple finish that is weather resistant, easy to apply and easy to refresh would be a blend of tung oil (10%), boiled linseed oil(40%), turpentine (25%), spar varnish (25%) (NOT spar poly), plus a little exterior oil stain (like Cabot's) to get a bit of color into it. If it won't be outside a lot, you can just get a small can of Minwax interior stain for the color. After you sand or wire brush the fuzz and splinters off the wood, brush the mix on liberally, let it soak in, then wipe off the excess before it starts to dry. Soak the wiping rags in a bucket of water so they don't spontaneously combust.
Gotta mix it yourself. Your part of this state may be different because you just have ARB but not SCAQMD rules to deal with, but in So Cal it is impossible to buy a decent exterior oil finish over the counter. The closest you can find to an over-the-counter product that would be halfway decent would be something like SuperDeck semi-transparent deck stain, but that will have a lot of pigment and still needs to be doctored to give the effect you seem to want. If I were to use that product, I'd still add BLO and turps, and probably a dash of Japan Drier to help it polymerize. If you are willing to order something online, look for a quality spar varnish from somebody like Jamestown Distributors or Fisheries Supply, and just thin it a little before you brush it on. That will give you a surface finish rather than a penetrating finish, but it will hold up OK. Remember that wooden boats get revarnished every year, but you won't need to worry about that unless your box sits out a lot.Do these mixes come pre-blended or do I mix them myself?