Hello Richard. A traditional Cuban mojito is made using white rum, which is often labeled as light rum or rum blanco.
When you visit the supermarket, head to the spirits section and look for a clear, unaged rum. Common and reliable options you will easily find include Bacardi Superior or Havana Club, but any standard white rum will do the job well.
I recommend avoiding dark, aged, or spiced rums for this cocktail. Darker rums bring heavy oak and spice notes that mask the fresh mint and lime, and they also change the bright, refreshing look of the drink.
For the best results with your dinner drinks, combine two ounces of white rum with fresh lime juice, fresh mint leaves, sugar or simple syrup, and top it off with club soda and ice.