Kevin, looks pretty good to me! The WB does look a bit off. Not surprising, the LED's make it tricky under the best of circumstances.
For WB, try going into your menu -> settings -> WB -> and set temperature to 10,000k - I'm almost positive you can do that with the 60D. That will get you much closer. Have you added DPP yet to your computer? If you shoot in RAW, you can do further adjustment with the "eyedropper" tool - select a pixel that is roughly 18% grey - you may have to pick, undo, pick and undo until you get the closest approximation. You can adjust the sharpness and contrast too (if shooting in RAW, the image may be devoid of contrast compared to what you see on the LED screen, which will have contrast added).
One of the hardest things to do is to jump to a SLR camera from a point and shoot with the "live view" feature - most of the custom features won't allow you to use it, because your eye should be in the viewfinder looking at the meter at the bottom of the viewfinder display - you need to look in here and properly meter your shot (get it close to the 0 or maybe underexpose to a full stop, i.e. -1). Don't get in the habit of shooting in manual with live view - you'll improve faster if you leave it behind and use the viewfinder - you'll quickly get used to it!
Shutter speed and aperture are only related in that the larger the aperture (the lower the number), the lower the shutter speed you can get away with for a properly exposed shot because more light is hitting the sensor. The higher the Av number, the less light that is hitting the sensor and you'll have to drop the shutter speed to get a shot that is exposed properly. This of course if for a constant ISO. The Av number is going to give you your depth of field. You could shoot at the same Av # (say 5.6), and get the exact same depth of field by using an ISO of 640 and Tv of 1/50 as you would with ISO 800 and Tv 1/40 (these are just examples). The lower the Av number (the more "wide open" your aperture blades are and the larger the opening), the thinner the depth of field. Also, the more difficult to get that very thin part of field in focus. Try lowering your Av number way down, shooting handheld, and take a pic of a tip of a coral - very difficult because such a small portion is in focus, that you shake enough to throw off the focus onto a different part of the coral easily through just breathing. For low Av # shots, try using a tripod and set your timer to 2 secs - your results will dramatically improve! Anyhow, try some shots at Av 5.6 to 11, and you'll get some great shots... (adjust your Tv and ISO to get it metered correctly, roughly -1 to 0). Once you master that, then lower the number and really hone in on a specific coral tip, polyp, etc. and the rest of the image will blur out behind creating that pleasing effect known as bokeh! Anyhoo, happy shooting - the more you shoot, the better you'll get. HTH.
