It was three years ago that I bought a "compact camera" from a well-known German retailer in most UK towns ( 4 letters, begins with "A" ). It was £30, I seem to recall. It is only certain times that the cameras are stocked ( "special buys" ). It has a MAXIMUM resolution per picture of 15 megapixels, but there is a choice via a menu of selecting lesser resolutions, so it can be set to the 300 that someone mentions ( above ). There are an amazing number of settings that CAN be selected, or it can simply be left to default. There is a flash that can be switched off if desired, "red eye avoidance", automatic contrast and focal length... so even a silly old fool like me can use it... The images are recorded to an SDHC card, that can either be taken out and placed in a computer card reader, or left in-situ and read via a cable to a computer, when the camera looks to the computer as an "external drive". The camera can also act as a video camera for the computer. As regards charging, the camera does have a charger, but also charges via the USB cable when plugged into the computer. The camera battery is not permanent, i.e. can be changed if needed, but normally lives in the camera to be recharged as needed. An indicator on the display says how much charge is left.
So the first thing is that the modern small household cameras like mine are quite sophisticated devices, able to cope with all of the normal family situations, and do come with facilities to recharge the removable battery when it is in the camera. There is even a thread underneath the camera for use of a tripod ( recommended for people portraits, as the camera is light, and easily "waved" when pressing the shutter ) . There is also a timer to get into the picture yourself.
It is, however, a family camera. It is not a professional camera, but if you just want a "record of family life" and for social media, then it is ideal.
So look around at those types of camera, readily available at all retail outlets... John Lewis, Curry's, Argos, Tesco... To see a WHOLE range, starting off with these cameras and going up to the professional ones all in one shop, then obviously it has to be somewhere like Jessops or similar stores ( I think they are still going ? ).
Lastly, you may not actually NEED a camera, if you have a smartphone. The cameras on smartphones are now very good - in many cases BETTER than the cheaper cameras - so take a look at your smartphone, and maybe save a bit of money ?
Happy photography anyway !