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I bought a cheap Olympus D545-zoom a while ago and played with it until I got familiar with it. After I got comfortable I stepped up to a Canon A610. So I guess I'd start small and work your way up.
Your problem look like lighting problems to me.The second one is not enough light and, you may need to set your White Balance manually or, use one of the presets for the particular type of lighting. What you need is a white or, light gray card to set the WB manually. What the does is tells the camera the lights temp for it to compensate. Also you might try using diffrent manual settings, like changing shutter speed and, apature. After all the great thing about digitals is if it doesnt work dlete it. Oh and, the problem with the girls pic is the bright light is to indirect and, the camera isnt compensating for it. That is why you almost always have to post process. Right now I have a ton of pics that need some post processing but, Im procrastinating on doing it.