I also would like to build it with him as it could be a fun project and get him into some practical side of things
Yes. A thousand times yes. It will be a great experience for both of you.
In an ideal world, he would be in the £300-£350 range leveraging used and potentially new parts.
I agree with @pastymuncher: unfortunately you'll need to basically double that for new parts, and £350 won't buy you much of a used PC either.