500 yards is really not difficult at all with a bit of practice. I do not know what game you may want to hunt but there are many cartridges today that can work within your given parameters and work for species up to elk. I personally would go with something that is easy to shoot well with tolerable recoil. Something ammo is readily available and affordable. 308, 7mm-08, 6.5 CM, 270 Win, 30-06 or something along these lines that he can afford to shoot and practice with. I have a Nightforce SHV 5-20-56 that has been a good scope and is also made in smaller sizes. My two Sightrons also work well and track really well and won't break the bank.
Tikka's theses days are a solid bet to shoot well straight out of the box.
Tikka's theses days are a solid bet to shoot well straight out of the box.