I’ve used quite a few different oils for something like this.
I like Tung oil and it provides one of the best water resistances for an oil finish, but it has a yellow appearance like linseed oil and does change the color of woods slightly. On something like Walnut or cherry, I think it really helps it. It brings out the grain and makes you see the depth more. On maple, however, it will amber it a little. Also, it has an odor. I don’t find it to be that bad, but some might. (I don’t like the smell of boiled linseed oil.) Also, I’m talking about pure tung oil.
I used mineral oil a lot because it is pretty much odorless, doesn’t hurt your hands to apply even without gloves, and is totally food safe, as @Jules mentioned. (It is an old timey laxative) It doesn’t bring out walnut grain quite as much as tung oil, in my opinion, but it sure doesn’t yellow the lighter woods like maple or birch.
I like to soak/wipe it on, let sit for about 15 min, and then wipe all excess off. Then, let it rest for 10+ hours. Then, do it again. If this is just something to be worn like a pendant necklace or something, you might not need a second coat. I only do that on the cutting boards I make so they have the max conditioning right at the beginning.