Why not just buy a 700P in 308 up front and bypass the upgrades.
They come with HS Precision stocks with full lenght alum beding and now a adj 40X trigger. All for alittle over 800 and change. With a good set of rings and a base along with bottom end optics its not that much over budget.
And he will have a rifle that's much better up to the challenge. And if it ever gets sold it will be much easier to sell in its original form and it hold much better value than a home built parts gun.
For the OP's intended purpose this would be a good start. I personally don't care for the HS precision stocks because of the comb height but are a good upgrade from the junk tupperware that comes on the cheaper rifles. When I bought mine I gave $550 for it (same one as in the add in OP) with all intentions in upgrading the parts over time. It went in stages where is sat in a houge stock then in a B&C M40 stock, now in a mcree G5 chassis. Also changed optics several times starting with a Vortex CF2, ss16x, Primary Arms 4-14, and finally a Vortex HD Gen 1 5-20. Also upgraded to a Timney 510? About to order a barrel in a couple weeks so only thing I will have left is the action from the original gun. Lots of lessons learned but am happy with the(almost) finished product.