There is no doubt the synthetics offer superior protection. And, it can be used to break in a rebuilt engine. The Corvette & Vipers and some other cars come from the factory with synthetics. However, if you have a carbureted car and are not pushing the extremes on temperature etc, I would use non-synthetic oils. The reason being is that older carbureted cars tend to get the oil dirtier quicker. The oil has not broken down but rather gets loaded up with fuel blowby due to larger tolerances, and more water condensation. So I would not recommend extended intervals possible with synthetics due to the contamination reasons.
Diesel oil is fine for non-catalytic equipped gasoline engines. It's rating is superior to gasoline engines with regards to anti-wear additives. Keep in mind though, that if your engine burns a lot of oil, these antiwear additives will also burn and build carbon in the cylinders. As mentioned previously, they help shorten the life of a catalytic converter if too much oil blowby is going out the exhaust.
By all means, use a detergent oil. The development of detergent oils and the PCV systems are a large reason that you do not see the sludging of oils that was present in the 50' and 60's.