There's a thread
here that helps explain why some batteries work and others don't.
As far as rechargeable batteries and chargers in general, the best information I've found so far is actually in product review comment threads on Amazon, if you have a couple hours to read them all. Start
here and go through all the pages of comments, then repeat for NLee the Engineer's other charger or battery-related reviews.
If you don't have the time or inclination to sort through all that, just follow the specific recommendations of people here.
I'm personally using Eneloops with no complaints. I've had no-name alkalines fail to even turn the camera on. It's a bit picky.