From the not-very-detailed pictures, it appears to be a Remington 700 ADL (blind magazine) in an aftermarket stock. Depending on who fitted the stock, that could be either a good thing, or a bad thing.
Look for an evenly inletted barrel channel - no inletting by a blind man with a dull hatchet-type stuff. It appears that the trigger guard is standing a bit 'proud' of the stock (sitting on the stock, rather than in the stock). Also check to see how stiff and hard that old-looking recoil pad is. If the recoil pad needs to be replaced, that's a minimum $40-50 job.
If the inletting is all jacked up, you're looking at a lot of work to make the thing look decent. You can do it yourself with a glass bedding kit, or pay a gunsmith a bunch of coin to do it. Also check the stock for cracks at the rear tang and on the butt.
As noted earlier, the bluing has been removed from the bolt shroud for some reason. The blue is also worn almost completely off the bolt handle. Methinks that rifle has been shot a great deal.
I'd recommend taking a bore light with you so you can examine the bore. If it's extremely dirty, walk away. If he says 'It'll clean up,' walk away. If the crown is worn or dinged, walk away. If the bore is pitted, walk away. Make certain that the safety functions correctly. If the trigger is adjusted to a 'hair' trigger, I'd pass - there's no telling what other improvements Bubba made.
Of course, check out the scope for clarity and ease of adjustment. Look for condensation on the inside of the lenses or anything else obstructing your view.
Ask the gun shop owner if he has a 'No-Go' headspace gage, and will check the rifle for you. A .270 uses a .30-06 gage. If it doesn't pass the headspace test, RUN away!
Good luck!