Hi Aaron,
for a thread on setting the White Balance properly have a look at
http://www.scubaboard.com/t71029-manual-whitebalance-c-5060-.html. It has a very useful link that AndyT posted yesterday.
As regards the settings. Play about with which mode you like best before you even dive. I like Manual (M) but others prefer the Aperture priority mode (A) and the Shutter Priority mode (S). I like M as it allows me to play with the shutter speed and mess about with the aperature. If you just want to have more light/less light in your pictures choose the S mode and play with the shutter speed. The faster it is, the less light but anything below 1/100th of a second may result in blurring.
Set the camera to Autofocus but turn fulltime auto focus off, and set the focus to SPOT metering. Fulltime autofocus slows down the shutter time so you may not get your shot. Also get used to half depressing the shutter before shooting so the camera is in focus before you depress all the way. Not doing this often leads to blurring.
Turn on the option for the marine accessory when you're using the housing. No one seems quite too sure what this actually does but might as well use it if it's there
Set the ISO to 80 or 100 - AUTO tends to give grainy shots sometimes as it sets the ISO too high
Unless you're very close to a subject don't use the flash, as otherwise you're likely to get a lot of back scatter.
Turn off the auto reset of settings so that you don't have to remember to change everything every time you use the camera
Play about with MyMode. Many swear by it.
Have a look in the forums as well for other useful tips that apply to the 5060 and other digital cameras
Cheers