I know what you mean. I figure the future grandson will get my son's 1st rifle, the H&R handi-rifle.We all have a budget to work within but I get a little sentimental in these deals. This is likely the gun he will hand to your grandson.
https://www.budsgunshop.com/catalog/mobile/product/79536/ruger+american+308+win+black+synthetic+6903
So, I’d stretch my budget look for one of these in .308.
https://www.budsgunshop.com/catalog/mobile/product/83151/ruger+amer-s+243+all+wthr+mtss