put up first!
Yes, put up first unless so you can control who plays who in the 4th AND 5th match... if you only need to win one, you play your stronger player on the weaker one. Need to win both, then you match up best you can.
Also, if you have a great high end and want to make sure they get the other teams top player, you can put up a low end on each of your turns, and unless they play their high on one of them, your top player will get their top player.
If your team or the other team doesn't have many options of what to play (lots of people with the same handicap), then let them put up first as control of the last two won't mean as much.