You're better off upgrading to iOS 10 first. There have been people on here that ran into problems when they updated the apps first and had to re-install them to get them to work after upgrading.
Uhh, no? It doesn’t. As long as you do both, the order doesn’t matter. Some apps may simply not work correctly otherwise. The problem mthomas refers to can always happen, with every program, regardless of an available app update. It is not particular to iOS 10.