The 1994 version did have 1-2-3 scoring. As for payments, the only way that's both reasonably fair and simple would be to divide equally and everyone get their own check. You start getting into who got the most answers right, played the most face-offs, got the most points in Fast Money, etc., and it just gets impossible unless one player was a complete idiot.
On positioning, well... I'd still put the weakest player last, assuming all family members are pretty close on buzzer speed. You might not even *get* to five rounds. Even if you do, the Face-Off is relatively easy: no answers are taken already, and by the triple rounds the #1 is usually obvious. But the second and third players often get to answer twice in the early, longer rounds, and if they do go to five questions, after the Face-Off you're back at the front of the line again to finish up.
Now, if everyone's good at the game but one or two have pokey hands (keep out of the gutter) then put them first.