In decent daylight, the image quality of the D60 at ISO 800 is pretty decent. Even ISO 1600 is not "that bad" as long as the light level is moderately high, but ISO 800 is a notch better of course.
The larger the image is, and the more at right-angles to the camera, the higher the shutter speed needed. If you want to get ball-on-bat shots shot from either the 1st base or 3rd base areas, you need a shutter speed of at least 1/1000 second to keep the ball round.
1/250 second will not freeze a lot of motion fully, but it can sometimes give a nice looking bit of blur on the ends of things, like the feet, the hands, the end of the bat, or the baseball moving through the air.
If you shoot action coming right toward the camera, like a kid sliding into home plate from the area by the backstop and looking down the 3rd base line, that type of direct, at-the-camera motion can be stopped by a slower speed like 1/250.
The essential thing is to keep the ISO high enough to get a FAST shutter speed. With an 18-55 kit lens, a "fast" speed could be 1/250 second; if you have a 55-200 zoom, at longer lens settings, "fast" becomes relatively higher in speed, such as 1/400 to 1/1250 second. Look thru the captures and make sure the shutter speed is freezing the action by zooming in on the LCD review screen and looking closely at the critical areas--ball,bat,arm,etc. and seeing if the action is frozen, slightly blurred, or heavily blurred.