Pennzoil air cooled would be my choice for break.
I believe that synthetic oil is to slippery for a good break-in.

Remember that the heating and cooling of the engine is the major part of breaking an engine in.
Run it until it gets good and warm and then shut it off until it reached the outside temp. then run it again.

5 or 6 of these and your ready to start working the saw. 3 or 4 tanks of gas and it's broke in.