Limiting self to AA you’re looking at older cameras or ones that somehow combine a small basic sensor with a short battery life for the price of a much better camera with rechargeable battery.
AA powered is not as convenient as may seem, and can be costly in consumables.
For my money in yr position would grab a Lumix TZ55 currently on sale for I fhink £104 in Argos which IMO is a bloody bargain for that much camera. and if you want USB charging add a replacement usb charger (£11-ish). Bang tidy!
I use an RX100 compact that charges via USB, in normal use a charge lasts me all day, but if I’m away for extended periods I take an Anker 13000mah USB powerpack with me, gets quite few charges in if away from the mains (ie wild camping or a heavy day photography out in the sticks)