Tyre choice is indeed extremely important and Swiss Side has spent a lot of time investigating tyre performance. For triathlon, aerodynamics is by far the most important performance parameter. In this respect, choosing a tyre which provides the best aerodynamic performance for your wheel is a high priority, in addition to rolling resistance and puncture protection. The sidewall tread pattern on the tyre is actually very important due to a complex aerodynamic effect called the „boundary layer transition“.
The best aerodynamic tyres on the market right now are the Continental GP 5000 and the Schwalbe Pro One TT (either in tubeless or tube-type versions). The worst aerodynamic tyres (only important for the front wheel) are slick/smooth tyres with no sidewall tread. These tyres will destroy the aerodynamic performance of any wheel from any brand. Tubeless clincher tyres offer lower rolling resistance than clincher tyres with tubes. This is important because power is power, whether that be aerodynamic drag power, or rolling resistance power.