What is the lowest shutter lag time on current dslrs

Shutter lag is not what you have to worry about.

Go to a shop and get a feel for the auto focus. I don't know how good it is on the d3000 but try it out against a couple of other cameras in the same price range. What you need is something that locks on fast and seems responsive - and if you could try the sport setting outside with moving objects (cars or similar) that would be even better.

Another thing to think about is pictures (or frames) per second. The d3000 with 3 fps will probably do just fine for what you need but there are of course faster (and more expensive) options available.

Bo