If you go for "less stops is better" there is choice in connections via AMS or CDG with Delta/KLM/AF. That means US immigration in MSP, when you're tired, but delays are less important. There are three flights daily between AMS and MSP, so you can go for minimum connection time if you don't have the last flight of the day.
To earn miles on Star... I saw United options with one stop in EWR or IAD, meaning meeting immigration there and risking to miss the connecting flight, so check connection times and not taking the last flight of the day. Also try to find out whether the connection requires bussing between terminals or just a comfortable indoor walk.
There are several options with two stops: Air Canada, two stops in Canada; LH(+UA) via FRA and ORD... Pick the airline or route you like there. BTW, prices in September are much nicer than with departure in August!
It would help if you tell is what you value (comfort vs. time vs. entertainment vs. free drinks) in what you seek and whether there are budget constraints or you want to fly business or first.