Ultimate Racer provides all of your software requirements, but for the timing system, you will also need some hardware to detect slot cars on your track and pass that to your computer.
There are many, many options for slot car sensors, too many to list in detail here.
For more details, please go to the Help section.
Below is a brief outline of the most popular ways to hook up your track.
A simple home made or adapted bridge with lights that shine onto the track. Set into the track are photo resistors which detect when a car passes under the bridge and casts a shadow. The photo resistors connect to a parallel port on your computer.
A modified section of track which has a few centimetres where the rails are unpowered and isolated. This connects to a simple electronic circuit, which in turn connects to the parallel port on your computer.