It's a little early for me to finalize any new year's resolutions; although I think you've picked a good project for your son. I've done lots of origami in my life, and although I was never notable in the origami communities, it was my notoriety at school for a while [fidget spinners weren't a thing, although math teachers got a kick out of seeing a new model appear by the end of each class].

I recommend avoiding dedicated origami paper. If you need squares, teach your son how to cut squares from printer paper. It's both cheaper to buy printer paper in bulk, and mercilessly rewards accuracy early-on. Paper specifically manufactured for origami can be a nice present after he has the skill to make good use of it.