Most true digital compact cameras have balances that help fix the color situations based on lighting. The only time EVER and I mean ever that you will get true color in an image without outside aid is if are taking a photo outside on a very bright and sunny day (during hours of 10a-3pm).
Any other time the sun, clouds, indoor lights will cause the colors to change from their natural color. Cloudy or dark lighting give off blue tints, tungsten indoor lights give off amber lighting, fluorescent a greenish color. So it is best to use a real camera that can handle converting those tints back to the correct coloring. No amount of lighting will fix these tints.
But you can always use a photo editing software to fix the coloration issues. Photoshop has photo filters that fix coloration issues pretty well and with one click of the button, or you can sit there and fiddle with colors. But these softwares are expensive, so best to use a digital camera
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And if you are looking to get a new one. My favorites are Canon or Sony. They tend to have very good saturation and color balance which helps with all of our color-based photos.
If you have any photo questions, don't hesitate to PM me. I'm in a hardcore photography class right now for school and learning all kinds of tricks.