I actually doubt you can play modern games on Pentium(n gen) , it is supposed to be processor for entry level desktops with moderate usage and lacks an essential Intel feature : Hyperthreading which is necessary to run modern softwares / games.
So an i3 is still a good bet for future proof config and by the time he upgrades the procy and ram, he might have to upgrade whole config.
He can cheap out on ssd, since the budget he got can mildly cover the 1tb hdd
And, I think RX 460 is best bang for buck for now and atleast good enough to handle new games at 1080p resolution if op desires for it.
PS 8gb ram is bare minimum this days for any game.