The probe was suppose to do 10% lightspeed. The 61 degree inclination trajectory was to put it on a path to A. Centauri B. The report does call for a heavy launcher capable of putting large bulky payloads into orbit. I'm guessing a 10 meter wide launcher with a 200 metric ton payload. It also calls for a large station to be used as a shipyard for assembly and flight prep.

My ideal launcher would be a improved Energia. Increase the diameter from 7.8 meters to 10 meters and scale the length accordingly. Then add a 5th RD-0120 main engine. I'd also increase the number of Zenit boosters from four to at least six.