For family snapshots, you're probably better off with a new phone with a good camera than a dedicated camera like a powershot these days. The image quality is getting surprisingly close, and the availability difference inherent in having your phone's camera in arms reach all day every day will likely lead to capturing more interesting moments. The latest iPhones are a safe bet, and some androids are getting pretty good these days as well, but you'll want to research the exact model you're getting to make sure it's one of the good ones.
If you're really interested in quality, you can supplement your phone with a DSLR for events when you know you're going to be taking pictures. Or for special events you could rent equipment from your local camera shop, or hire a photographer.
There are interesting things coming down the pipe in terms of multi-lens and light-field cameras, but if you're thinking in terms of saving things for posterity, you might want to be conservative about that sort of thing until they become a bit more mainstream and standardized. Remember, they had 3D cameras back when you were a kid too, but when's the last time you looked at an old stereo-photo?
I'd also recommend you read up on shot composition, lighting, depth of field, speed, aperture, etc... And mabe take a photography class. Understanding how to take a good photo makes the difference between boring and beautiful.