What two shutter speeds are considered best to freeze motion?

Very generally, higher shutter speeds are better for stopping or freezing motion: 1/500 or 1/1000 of a second and up if your camera goes there. But you must bear in mind that all motion is relative.

For example, say you are standing at the side of a road wishing to photograph a passing car. The car is going, oh, 40 mph (64 kph). As the car comes level with you, you click the shutter at, say, 1/1000 of a second. This will probably stop most of the motion of the car, but depending on how close you are to the car, there may still be some smearing of the car. But motion is relative: If you shoot the car while it is still approaching, 1/1000 of a second will probably freeze it pretty solid.

But suppose you pick up the car in your viewfinder (not all cameras can do this due to what is called "shutter lag") and follow it, clicking the shutter as it passes in front of you and "following through" like a golfer after the swing (this technique is called "panning"). You'll be surprised. Done correctly, the car will be sharper, but the background will start to blur a little. Continue the experiment by slowing the shutter down. Try the same trick at 1/500, 1/250 and on down (remembering to close down your aperture if you must do so manually). What happens? How sharp can you hold the car? How much does the background blur? Do you get an increasing impression of speed? Try this trick with your kid going by on a tricycle. You can make the youngster look like s/he's at NASCAR!

Another example: you're at the skateboard park and a boarder is flying up the ramp into the air. There is a moment, a very short moment to be sure but a moment in time where that fellow essentially stops moving, right at the top of his arc. A shot timed for that instant can be made at a remarkably slower shutter and still "freeze" the "motion" because, at that instant, there isn't much motion. Obviously this takes timing and a camera with no shutter lag, and it's usually a lot easier if you crank it to 1/500 or so, but try slowing your shutter and timing your shot and see how much more of an impression of motionyou can capture in a still photograph. There will start to be some smearing of the skateboard as it rotates, the hands and arms may smear, but that's what gives the shot the feel of motion in a still picture. This all takes what a friend calls "spray and pray" but just keep shooting and you may be surprised at the results. (Tip: this is not necessarily a job for your 80 fps motor drive, even if you have such a thing. Use finesse. Shoot for what Cartier-Bresson called "the decisive moment.")