Different Types
WPA Radius Authentication - Your typical home user wont use this, unless you want to setup a radius server. This server works with WPA to pass different keys to each user. I'm not going to go into how to set this up.
WPA PSK - PSK stands for Pre-Shared Key and is most commonly used by home users. The user must have a certain password to enter the network. PSK can be used with either AES or TKIP, depending on what your hardware can support. It is important that you choose a strong password to prevent against dictionary attacks.
AES - An algorithm that requires special hardware support to use. It is stronger, but a firmware/driver update won't get you AES.
TKIP - This system changes the key every specified amount of time to prevent cracking attempts. You can usually adjust how often it changes in the router/AP settings. This does not mean it changes your password, just the key.
WPA2 - The new WPA standard that uses a stronger algorithm, but is not backwards compatable with older hardware.