You can get a really small feature rich camera very cheap these days. I picked one up a Fujifilm a couple years ago. I can change shutter speed, aperture size and (simulated) film type. It has dozens of different shooting modes including high speed for slow motion shots. 15x optical and 50x digital zoom. All for about $125, I think, maybe less. Something like that would work. Can pick up one with less features for less of course. I use my phone for spur of the moment photo ops, but when I go places that I may wanna take pictures I will have my camera ie festivals, zoos, parades and so forth.
I would say definitely look for one with high speed capabilities and adjustable shutter speed. Good optical zoom over digital zoom.
Mike