As someone who played through the game with the minutemen I can say that as a whole the faction had some sort of... Underwhelming quests in terms of narrative. It had a great feeling of progression though, making it feel like the most humble of the factions by not particularly targeting the other ones. While I did have the minutemen assist me with the Institute, it was my characters desire to do it, not any of them. It makes the most solid moral compass decision in my opinion, due to the lack of harming anyone who doesn't "have it coming" (basically hurting/kidnapping,etc.)
I suppose I'd say it was sort of a bore at times, but it did give me a good satisfaction to know I personally made myself into the leader of a influential faction by simply helping the people of the commonwealth.