$300 is a good neighborhood to explore.
Since you have not given us much to go on except price, I am going to make a suggestion.
Canon SX130
Take a look at that camera and tell us what you think.
It is a step above the usual point-and-shoot
It takes excellent pictures and gives you room to grow as a photographer.
You should be able to find one for around $250.
Here is a full review with sample photos:
http://www.steves-digicams.com/camera-reviews/canon/powershot-sx130-is/canon-powershot-sx130-is-review.html
..
I'd like it to be a little better than my tiny point and shoots that I've collected in my junk draw. I'll be mostly taking photos of my children. I'm jealous if my sisters beautiful Nikon but, I can't afford a 600.00 camera.
Thank you for all your help! I'm really overwhelmed with the choices.

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