DmC is actually an alternative universe, so it's not really connected to the original series (in fact in the Downfall DLC you can see a scene which is pretty similar to the one in DMC3, where Vergil and Dante fight against each other). But yeah, it's nice to see Dante's brother on the good side at least for a bit!
I heard the second game is more a standalone thing, where Dante is not really Dante, but Vergil who took Dante's place after his death or presumed death. This would also explain why in the second game Dante looks so serious... he doesn't actually look like Dante at all, but more like Vergil indeed speaking about the personality. So I too think the order is: DmC (alternative universe, not really connected), DMC3, DMC1, DMC4.