Your engine calls for GM 6094M spec oil. The M1 5w/30 and 10w/30 conform. The 10w/30 product is not labeled with the newer 4718M spec but.... If I had the LS1 I would use M1 10w/30 especially in the summer where I live - it is HOT, - and the Delco filter. I like the M1 filters too.
Synthetic oil and breaking in an engine is a myth unless the engine has a flat tappet camshaft, then I would use a high quality Dino oil of low viscosity for the 30 min run-in on a new cam, then out it goes for synthetic. Roller cams do not need this precaution and many would argue that a flat tappet setup does not either, but Crower and Edelbrock recommend no synthetic on their flat tappet new installs, no such warning on the roller type. Given the cost and difficulty of a new cam install, my new little Chevrolet 327 build will get good ole Pennzoil for the break-in, then back to M1 10w/30 as soon as it has 30 minutes on it.
My LS2 has had M1 in it from day one and will never have anything else in it. It uses zero oil and has never required a top up between changes. It has 9100 miles on it, the oil is as clean as a whistle and will go in for it's second change at 10K.
FWIW