[Nonfractal]

Gordon, 
The trick of timing is to get all of the components working and working together.

Sit down and work out how it will all be wired up. 

Arduino: buy, fit it in a box and upload the code to make it work
Gantry : design, build and fit led emitters 
Start line: fit optical sensors into the track.
Laptop : get one   then load race coordinator 
Spend time learning the software 

AlanW