If your definition of point and shoot lies on how the camera will automatically choose the right exposure for you and also auto focus on the subject, I could give you several suggestions that match your budget criteria:
1. Olympus Mjuii
2. Canon Sure Shot supreme
3. Nikon lite touch AF zoom
4. Pentax Espio
Or you can just go to your closest thrift store, they usually have one in the inventory.
One thing about point and shoot is most of them are the same. They are all dependent on their electronics and often times the only thing that differentiates them is their lenses, be it focal length, or how fast it is. The idea of having a point and shoot is to expedite the the time that you spend setting up the camera so that you won’t miss that “decisive moment”. Since they are all mostly electronics, somehow think of them as disposable. Once they break, wellp thats it. So in my honest opinion, it doesn’t matter which one you get. Don’t over complicate your selections, just go get a cheap one from ebay or your nearest thrift and start shooting!
Cheers,