Directly from Briggs and Stratton. Their number one recommendation is 5W30 Synthetic followed by SAE30. I would myself go buy a 5 qrt jug of Mobil 1 5W30 Synthetic High Mileage oil at Wal-Mart and then have several oil changes and top off oil available.
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Oil Recommendation
Synthetic 5W-30 -20 to 120° F (-30 to 40° C) provides the best protection at all temperatures as well as improved starting with less oil consumption.
SAE 30 40° F and higher (5° C and higher) is good for all purpose use above 40° F, use below 40° F will cause hard starting.
10W-30 0 to 100° F (-18 to 38° C) is better for varying temperature conditions. This grade of oil improves cold weather starting, but may increase oil consumption at 80° F(27° C) or higher.
5W-30 40° F and below (5° C and below) is recommended for winter use, and works best in cold conditions.
Type of oil to use
Use a high quality detergent oil classified "For Service SF, SG, SH, SJ" or higher.
Do not use special additives.
Choose a viscosity according to the table above.