Not sure Madlot is correct, the Precision is a lighter weight shoe than the Wave Rider. Precision is more for faster paced running and racing. The fact that you are light means you could get away with Precision for your general training, but as you've had shin splints I would suggest erring on the side of caution and going for the Riders.
Go to a shop and try them (and other shoes) on though, different shoes suit different people