Well, for lighting you can't beat natural outdoor light or natural light from a window. It is the easiest and cheapest light you can use. To really get some control over natural light you should look into buying two things, especially if you want to shoot portraits. You will want a diffuser to diffuse direct sunlight so it isn't harsh and so that you don't get hard shadows. You will also want a reflector to bounce some fill light into the shadows.
An overcast day can be great for shooting people too as you get really soft light and no shadows. But for a sunny day, the early morning or early evening light is best. Try to avoid shooting portraits in the middle of the day without a diffuser unless you can get the subject entirely in the shadows. Unless to do otherwise would work better for your image.
As far as angles go, a straight-on angle is usually better for shooting children than an angle from above their heads. Get down and get close for a dynamic portrait.
Fill the frame with the subject rather than leaving a lot of empty space. And think about the composition before you press the shutter button. I know that sometimes you have to act quickly but with a lot of practice it will come naturally to you to compose your shot quickly and still catch the action. I have toddler who I shoot a lot and it really has become second nature to really compose the shot rather than just shooting off in machine gun style. Even though I could shoot on continuous mode with my DSLR I don't. I have the drive mode set on single frame and it really has made a world of difference.
I was intimidated for a long time to try shooting in manual mode. Even trying aperture priority took a long time. I had my 35mm SLR for at least 2 years before I left the fully automatic modes. I was just afraid that I would ruin the shots. Once I had figured it out I was amazed at how simple it really was. So my advice would be to leave the automatic modes and see what you can do. If you have any questions about exposure just send me a message. I am happy to help.