The answers are in the FAQ.
In short, registered memory has additional circuitry on the signal lines that introduce a small amount of latency. The benefit is that you can add more modules to the board. Most dedicated servers and some workstatoins have registered memory. You need to have a motherboard that supports registered to use it.
ECC improves reliability by a small but measureable amount. If your machine will be used in a situation where a crash or data corruption is more than an irritation, or if the price of ECC and regular RAM are very close (<5%) then I recommend ECC over non-ECC. You need to have a motherboard that supports ECC to use it.