I second the suggestion of Linseed Oil. It is inexpensive, easy to apply, lasts a long time and can be reapplied from time to time to renew the finish. It is also a major component of many other oil finishes. I would also give a big two-thumbs-up to Birchwood-Casey Tru-Oil (which is made with Linseed Oil and some other components). Tru-Oil is also inexpensive and is a dream to use.
I have a can of "Boiled Linseed Oil" I've had around for years. Every couple of years, I apply a coat to the wood handles of garden implements (rakes, shovels, wheelbarrow handles, etc.) to keep them from drying out and starting to crack.