I see there’s 5k cameras, but it feels superfluous since mostly everything is 4K. Plus, unsure what device would be suggested for an amateur taking pictures and sometimes video of my nephews baseball games. He’s pitching if that has anything to do with the megapixels for videos and hoping to keep the price around $100-$150?
Photos and video are two different things.
A photo camera should be easy enough. Just get a used camera body with an option for sports shooting. The lens will probably be more expensive since you need a decent zoom to the camera.
For video, you may want to consider if HD is good enough. Do you really need 4k for baseball?