My son got a Crosstour action cam (cheaper Go-Pro style camera) for his birthday yesterday and it's been a massive hit. For £30 it comes with 2 batteries and loads of mounts, waterproof case etc. There's an app which you can use to view the videos over WiFi etc too which is fab (and saves faffing with memory card into laptop etc). Memory card is the only extra you'll need, but we've got him a few extra accessories for Christmas like a chest harness, selfie stick and such. We went out earlier with it mounted on his bike handlebars and I'm really impressed at the quality of the camera and video.
www.amazon.co.uk/dp/B073WWSYJK/ref=cm_sw_r_cp_apa_fabc_bM73FbE44FJBK?tag=mumsnetforu03-21
There's other models if you're wanting any extra features, better quality video etc, but for a child this is excellent, and IMO you get much more for your money than the VTech or similar versions.