Just got a rebuild 305, what type of oil should I use? Also what brand would be the best?

#1 is..... fully synthetic ..I use Castrol Edge

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The best motor oil to use in a new rebuilt engine is called break-in oil. a 5 - 30 for the first 1000 miles. Then change out the oil and filter, if you can, flush out the motor, then add what you want. either synthetic oil, or regular oil at a 10-3- or straight 30 weight. I'd change oil and filter after the next 1000 or 1500 mile3s again to make sure all the little metal filing have been picked up bu the filters. There are magnates sold that are on the oil plug or go around the lil filter to hold the metal filings. Read the above suggestion on the advantage of regular or synthetic. The brand? I'd go with a known brand, not a after market one made by "Jose's back yard oil well". The brand choice is a complicated as your favorite beer or car maker. Your call on that. My dad did not like Pennzoil for his reasons, I like Valvoline in my Corvette, but also use Castro or Pennzoil in my other cars.