I normally shoot in raw, this way I can leave the white balance on auto most of the time. Since all the information is stored, you can choose the correct white balance in Photoshop later, which is much better than doing it in the camera. Most of the time I use auto focus as well, with 51 autofocus points the camera has excellent auto focus, as long as the focus points are where you want them to be there is no reason to shoot in manual. (There are exceptions, but I will keep it simple)
I have ISO, F-value and shutter speed on manual when I shoot.
ISO: A low ISO will give you less noise and darker pictures, a high ISO gives you more noise and lighter pictures. How high ISO you can use depends on your camera, most cameras can use ISO up to 800-1600 without getting too much noise, you should test your camera to see what ISO levels are acceptable on it. Choose 100 or 200 in daylight and 800-1600 or more in low light situations.
F-value: A low F-value gives you lighter pictures and a low depth of field. A high F-value gives you darker pictures and a higher depth of field. A low depth of field means that less is in focus, this can give a beautiful effect called bokeh, where the background is blurry. A great effect for portraits, but sometimes you want more of the picture to be in focus, and you have to increase the F-value. How low F-value you can choose depends on your lens. Most kit lenses have a minimum F-value of 3,5-5, I highly recommend buying a 35mm F1,8 AF-S a 50mm F1,4 AF-S or a 85mm F1,8. These are relatively cheap lenses that are way more light sensitive than the kit lens. They give you 6-20 times more light than a kit lens, and I really like the bokeh effect. They are also better than the kit lenses in many other ways. If you don't have a focus motor on your camera you should buy an AF-S lens. What F-values you should choose depends on the effect you want and your lens. Some lenses have a big diffraction rate (more blurry pictures at high F-value). Diffraction starts at F-values above 5,6 and above F8 you may see a little effect on the sharpness. I normally shoot at F5,6-F8 in daylight if I want a relatively high depth of field and F1,4 in low light situations or when I want a nice bokeh. For a more detailed description with illustrations look at F-stops Explained
Shutter speed: A slower shutter speed lets more light reach the sensor and you get more light in the picture, a faster shutter speed gives you a darker picture and is great if you want to prevent motion blur. How fast shutter speed you choose depends on how much light is available and how fast your subject is moving.
Rule 1: Start using manual settings.
I shoot in manual 99% of the time, I normally guess the right settings without looking at the light meter, it's a great exercise guessing what the correct settings are before you look at the camera. After shooting in manual and doing this exercise for a few years, you will know what the correct settings are without having to look at the camera.
Why you can't shoot in auto? The camera doesn't know the speed of your subject:
If you're trying to freeze movement you need a faster shutter speed. If you are in a low light situation, the camera will try to keep the F-value and ISO at safe levels to keep the noise low and retain the depth of field, but to get a fast shutter speed you may have to accept a little more noise or a more narrow depth of field. The camera has no idea how fast your subject moves and can't adjust the shutter speed to freeze the action. You can solve this with shutter priority as well, but before you know the right settings yourself I would shoot in manual.
The camera doesn't know what your subject is, or how much you want in focus.
How you separate your subject from the background is very important, if you take a portrait you may want to have all the focus on the person and choose a low F-value. If you are shooting landscapes, you probably want to have more in focus, then you should choose a higher F-value.
If you shoot in auto you don't learn much.
I have met "photographers" who always shoot in auto modus (program mode on more expensive cameras), they may be very good at composition and lighting, but some of them never get the intuitive understanding of how the different settings affect a picture.
You can of course shoot in aperture priority or shutter priority, which are more intelligent settings than auto, but I would still use mostly manual settings until you can guess the right settings without looking at your camera.