On the original red is hot, black to ground. The new system the white is ground and the black is hot. So.... Old red to new black. Old black to the new white for grounds. If you are rewiring it all new, I suggest you run white/black to each, individual, fixture. Then the grounds all to a common grounding bus.
"If it can't be reduced, reused, repaired, rebuilt, refurbished, refinished, resold, recycled or composted
then it should be restricted, redesigned or removed from production."