Use your phone. Not much point to Point and Shoot cameras now, phone cameras do it better and are always with you. Perhaps the one exception would be a camera with a huge zoom range, like the Nikon Coolpix P-1000 with 125x optical zoom, but it isn't a thin flat thing that fits in your pocket, and it isn't cheap. It costs 2 or 3 times what an entry level DSLR does.
Found this quote, googling for point 'n shoot: "Ultimately, good point and shoot cameras worth buying are in the $500 range, bumping right up to cameras like the mirrorless G7. At those prices, unless physical size is extremely important for you, a slightly bulkier camera with lens options might be best, otherwise a new smartphone is likely all you'll need to carry. Jan 24, 2019"
If it is for stop motion, Point and Shoot cameras tend to be automatic everything, and usually not all those things can be set to manual, and sometimes none of them. (Or, like my last video camera before phones and DSLRs with HD or 4k video made them obsolete, they are auto but you can lock the settings, only it was really hard to find in the menu where they hid those functions.) So they will keep adjusting focus, white balance, and exposure, every time you walk in front of the camera to move the puppet. For animation, get an entry level Canon DSLR. They will have point and shoot options, but also manual settings when you want them. For the best quality still photos, same thing, use a DSLR. For easy to use and convenient, use a phone. Pro cinematographers have made actual films with iPhone cameras that look great, by selecting the lighting conditions where those cameras perform best. You can even do stop motion with a phone or tablet cam and an app like Stop Motion Studio. The app will lock the exposure, white balance, and focus, so they don't change during the animation.