I use Mobil One Synthetic 5-30W in my 1957 Ford with a 312 engine, the car has 42,000 original miles. Depending on your mileage, you may want to use 10-30W. My cousin always puts Castrol Synthetic in his four classics, including the 1957 Ford with a modified engine rated at about 600hp. I am sure that you will find people with a preference for a different brand but, in the end, I think that good oil is good oil.
There were no 350's in 1958. I would used 5W-30.
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