For NiMH rechargeables, you should just get Eneloops and not worry about the rest. If you can't find those, pick up some Eneloops, or possibly some Eneloops.
For LiIon Rechargeables, I bought some AW brand protected 14500 batteries many years ago. Those are still going strong and I highly recommend them. Recently, I bough some NiteCore brand 18650's and those seem very good, but I've only been using them for a few months. I'm sure they are from some other manufacturer and rebranded. But I don't know who. They are 3400mAh protected LiIon rechargeables. Lots of capacity there. I hope they last long. I predict they will, and hope I'm right in that prediction.