It can be a matter of taste. I prefer IMAP when the option is available, but it can have more overhead than POP and I prefer it for accessing mail across multiple devices (also if configured with idle it then has push rather than solely fetch capability). As to whether to leave on the server or not, if IMAP is being used, I prefer to if the ISP doesn't mind and provides enough storage, this way all devices have access to the same folder structure and things can be marked correctly as read when retrieving across multiple devices. If using POP, you will end up with everything fragmented across multiple devices.
It all boils down to how you plan to use it as that can make a big difference, such as across multiple devices, need for instant mail access, archiving, etc.
I didn't even think AOL still offered anything.