Clear pictures are a function of the quality and size of the sensor.
The quality and clarity of the lens
There is an excellent article on Wikipedia of all places on Image Sensor Sizes.
It's easy to read and will help you make a good decision.
All point and shoots have such tiny sensors they can not produce quality images when they need to be enlarged.
A good place to read reviews is dpreview.com which is now owned by Amazon.com
You can select models and read the professional reviews and read their forums to find out what people really think of the models.
The focus however is typically on DSLR's although once or twice a year they do a review of several point and shoot models.
I own a lot of cameras. My current point and shoot is a Samsung that was about $100 and I bought it for the video feature. It takes okay pictures for the money. Not as good as my old Canon Digital Elph. But Canon used to use larger sensors in their older point and shoots than they do today.