The most dominant player was Jim Brown. The best defensive players were probably Lawrence Taylor, Reggie White and Bob Lilly, in some order. The non-QBs who might fit best in today's league might be Jerry Rice and Deion Sanders.
But if this is about drafting to win a championship, QB is the primary. Phenomenal players at other positions simply don't have the same impact.
Brady is the obvious choice -- or Otto Graham. But I could make a strong case for Staubach, and if I were drafting, he'd be my choice. Staubach won a Heisman at Navy and took them to the Cotton Bowl long after the service academies were powerful football programs. When he was injured, Navy regressed to what would have been expected.
Staubach missed the most important years of his NFL career -- the formative years -- because of his military commitment. Had he joined the NFL on schedule, he almost certainly would have played in and won more Super Bowls. And he led the league in passing his final season. It is highly unlikely today -- given the difference in culture, pay, the end of Vietnam, etc. -- Staubach would be prohibited from joining the league when eligible. He would be much more valuable to the armed forces as an advertisement for the academy than as an active sailor.
I honestly think, given a typical career, Staubach would have won multiple Super Bowls -- as many as Brady and possibly more. His career was unique, so that can't be proven. But he is the best QB I've seen, and his game would fit in any era. He nearly beat the Steelers in two Super Bowls, and according to the voters, at least, basically half that team were Hall of Famers, along with their head coach.