I just got a new Toyota, as well. A Prius C. It also has the free 10k mile oil changes. I expect it's a great selling point for those that can't/won't do their own oil changes, but I'm not one of those people.
I've done the 1500 mile and 5000 mile oil changes, and will do 5k mile changes until the numbers even out. Then I'll start with 7500 mile changes to see what they're like. I've had trucks, too, and still do. I haven't done them any differently. Change regularly, with a good quality oil, at reasonable intervals. What more can anyone do?
I'm using 0w-20 M1 right now, haven't decided whether to stay with it or go with the PP 5w-20. I have used PP for a number of years in all the vehicles, but can't find it in the 0w-20 around here.
As for synthetic...define synthetic. How does Toyota define synthetic. If it says it on the label then it's synthetic. Remember, anything in an owner's manual is "recommended."
The big thing on the C section of PriusChat is the "0w-20 or your car will scream and die" people and the people who see it a little differently. The same car, same engine in Singapore shows the all-clear for 0w-20, 5w-20, 5w-30, 10w-30, 15w-40, and 20w-50. In SL, SM, or SN. When that came to light the 0w-20! people quieted down considerably.
I know some people are stubborn at times, but to complain about the oil you get for free at dealers intervals when you could easily do it right by doing it yourself seems a bit silly. It's just oil changes. And I can't imagine you'll void warranty by using something that is authorized and doing it at shorter intervals that "recommended."
Keep your receipts and keep records. If anything happens you'll have to fight it no matter what.