What's even better, is that you can simply connect the controller with a USB to the PS3 and let it recharge, no need for batteries or extra peripherals.
Also, put these games on your 'to play list' too(some console exclusives that are worth mentioning):
The Darkness
Dragon's Dogma
Little Big Planet 2(endless user generated levels that are sometimes even better compared to the levels in the main campaign)
Shadows of the Damned
No More Heroes: Heroes Paradaise
Deadly Premonition: Directors Cut(if you like twin peaks, there is simply no way you can let this slip by)
Catherine
Outland
Castlevania: Lords of Shadow
Demon's Souls
Battlefield: Bad Company(The original BC, it has an awesome main campaign and it should be dirt cheap by now)
That's about it for now
Deadly Premonition and No More Heroes have awful controls and PS2 like graphics, but the characters and the story in both games are simply amazing.