The i5-4460 will be perfect. It'll easily run games on max, if paired with a good GPU. It won't hold back your GTX 570 at all.
As for the GTX 570 and 6GB, those are still acceptable specs for games. Don't expect to put Crysis 3 on ultra at 60 fps on a GTX 570, but generally it still holds up well for 95% of games.
I'm actually getting an i3-4360 next, but I have other motives for that besides just performance.
In new and future games an i5-4460 will hold up better.