Welcome fellow Volunteer. That looks like a fine stick (from the bark, I'd guess Oak or Maple, leaning toward Oak)
I'm going to go against the grain here for a couple of reasons I'll get to in a moment.
I'm going to tell you to go ahead and make your shillelagh
First knock all that dirt off
Do you have a belt sander? If so go ahead and round that sucker off slowly with a rough grit paper. It will go quickly so, just try to take the outer edges off and see how it looks.
If not, with a nice sharp knife start whittling away the roots and skin from the top 6-8 inches. Don't try to cut too deep and always cut away from your self.
Depending on how green the wood is underneath, you may have a little waiting to do. If it is really green and wet, mix 50/50 dish detergent and water in a small bucket and put the sanded end into it and let it sit for a week or 2. Then take it out and let it dry for another couple of weeks. When you can, start sanding it with finer and finer sandpaper to the finish you want. Then start stacking Tung oil treatments until it won't take any more.
Then you can cut the length to fit your purpose if you desire.
Now for the reasoning.
#1 It's your first stick and you are raring to go and there is no reason for you to buy one. If you mess up, there are plenty more out there.
#2 Where you live, it is not arid or dry, The stick will dry slowly (unless you put it next to the fireplace) and shouldn't check very much.
#3 Experience is the best teacher. Once you have a feel for what wood does and is, the posts of this great forum will make more sense.
#4 You will not stop at 1

so once you get this one under your belt, you will be out looking for a stockpile
#5 You aren't selling it, it's for you and your son, a shillelagh is nothing but a rounded stick

(I know that technically it is culturally more, but in essence

)
Any how, get started get your son started and if you have any questions, shoot em out.