Barnes started every game he played last season (93 games total including playoffs). They almost never ran plays for him early on and even late in the season and in the playoffs they would only run something when there was a mismatch, which was frequently in the post season because teams threw the kitchen sink at Curry, Klay, and Jack (Lee was injured).
I don't think their signing Iggy had anything to do with what they think of Klay or Barnes. They had an opportunity to add an all-star kind of player, a guy who can be a secondary ballhandler, and a guy who can guard Durant, Westbrook, Kobe, Harden, etc. It looks like Iggy really is the defacto backup PG, so he'll start and play backup PG duties. Keep in mind Barnes also had success in the playoffs playing extended minutes at the 4 next to Bogut, and he put on 10 lbs this offseason in preparation for more work at the 4. So with Iggy playing the 1/2/3, Klay playing 2/3, and Barnes playing 3/4 they should all be up over 30 mpg. Bad news for the rest of the bench unit though, as I don't see anyone else sneaking into that wing rotation significantly (Draymond Green may get spot minutes at the 3).
As far as who starts between Klay or Barnes, its been a topic of conversation for W's fans all summer. I would rather start Klay because hes a superior defender and he spaces the floor better. Shooting is this team's greatest strength, why shy away from it? Harrison is the better one on one scorer so I'd like MJ to give him the green light as a 6th man. Apparently Barnes was tearing Iggy and everyone else up all summer in workouts, but hes looked like shit in his few preseason games (hes out now with some kind of foot ailment), meanwhile Klay has been VERY sharp. I suspect MJ may be fucking with Klay's head trying to get him to play with more of an edge, but maybe he really does see Klay as more of a 6th man type. Regardless, they'll both get over 30 minutes a game, and I'm guessing they'll both be closing games even though one of them will not be a starter.