I don't know this for sure, but I believe you will have to oil then wax the neck (wax would keep the oil from penetrating the wood, right?) That being the case, I'd apply the oil and see how it feels. You might be happy with just the oil. If not, then you could wax.
I like Danish Oil. Watco is the brand recommended to me by a first-rate luthier. Home Improvemnet stores sell it. From what I understand, Tung Oil is/can be very toxic, so handle with care.