What about a Gopro? They are quite sensitive to good light conditions but otherwise lens and resolution is very good, not DSLR grade but lots better than webcam/phone. Fisheye can be disabled. Audio is also decent, maybe not studio-grade indoors but when moving in the wind outdoors it's a lot better than phones or other non-professional gear. Lots of avilable mounting-gadgets and tripods available. Price is just above 300€ for last years 8-black model or sub 200€ for used or older models. Then you can use it for other fun stuff as well.