I don't think you need to change the oil at 3000 miles if you are using Mobil1. It is a very good oil that will easily run much longer than that. It's a synthetic-based oil that my friends tell me they run 15,000 miles between changes. They report getting 200,000 miles out of an engine with no oil-related problems.
The difference between 5w and 10w oils is really not that significant. The '5' means the oil will run more freely than the '10' at lower temperatures. The higher number, the '30' means the oil will lubricate at higher temperatures, to a point. That's why there are various numbers on the oil on the shelf. In your area of the country, 10w-30 is a wise choice.
The engine in your car will generate more heat than the old cast-iron engines did. I would reccomend using a '40' weight oil. GM has done a lot of un-published research on motor oils. My brother-in-law retired from there. He told me the absolute best oil to use in my Mazda engine, based on this research, was Valvoline.
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