Honestly, for your kid, you could get away with a 223 (or 223ai) bolt gun at most of these matches. Ballistics can be better than 308 and way less recoil.

For you I would stick to 6.5 Creedmoor (magazine-fed) and a 4-20 or 5-25 scope with first focal plane. 6.5 Creed will allow "off the shelf" ammo in quite a few flavors, one is likely to shoot. 3-15 should be enough scope depending on the glass quality. FFP is a must!

I would start at Hoser's match in Pueblo or CRC. Great people, fun time, lots of help (especially at Hoser's). Distances are not too far either. After that look at the Raton match. It is a great match, any you will love it. The ranges are 200-890, but most is 200-600, with a couple pokes out to almost 900. The Come out and shoot! You will have fun. You will learn a ton and no so much more of what you need after that first match.