Sorry...but you are NOT going to find anything that fits what you want for the money you want to spend. No way. For $125, you could get a cheap digital point and shoot camera, which is fine for snapshots. But not real photography. It sounds like you want to take a lot of action shots, and point and shoot cameras are horrible for that. The shutter lag will drive you absolutely crazy. You press the button, and 1 or 2 seconds later the camera will finally take the picture. Then you have to wait again for the camera to save the image file to the memory card. That obviously isn't going to work if you want to take photos to freeze action.
If you want to take a lot of action shots and want an affordable camera, then I'm going to suggest a 35mm SLR camera. (yes, FILM!) The reason is that mechanical film cameras have NO shutter lag. The instant you press the button, the shutter fires and captures a picture. It's absolutely instantaneous. That's the only way you're going to be able to take pictures to freeze motion. And you can find a vintage 35mm SLR in good condition for fairly cheap.
The only cheap digital cameras you'll find at Walmart will just be point and shoot cameras. They're fine for snapshots, but won't do what you want.
If you absolutely have to have a digital camera, then save up your money for a DSLR. But if you want a good camera right now that can take good quality pictures with no shutter lag, then get a 35mm SLR film camera. I would recommend a Minolta camera, like the Minolta SR-1 or SRT-101. The Pentax 1000 is another good vintage SLR camera that a lot of students use.
So you decide...$600 for a DSLR. Or get a good used 35mm SLR film camera that will take great pictures, probably for less than $100.