I would use 900 MHz Gen 2 style tags for the distance reading. Then you need a reader. I've used the ALR-9650 from Alien and it seems to be the best value for the money. It has the ability to mount a second antenna to read from multiple locations on the track. This allows serial and network reading. You might be able to get this going with Arduino, but it is going to be much faster initially to run on a PC. Setting up this with PoE to a network makes install simple with no local power.
This reader can be setup to push new tags it reads to an IP address, while constantly scanning. It will queue up the tags and feed a stack of recently seen tags. Individual label tags can be under a dollar. You would need to make sure that they are placed away from metal (which shouldn't be a problem on RC cars, with mostly plastic bodies.)
I'm talking to this reader with a simple Python script over ethernet. We will also be using it to detect when things get close and send indications to an IP address.
http://www.alientechnology.com/readers/smart-antenna/