So what oil SHOULD be used with a new engine AND why?

I bought Wolfs Head straight 30 weight non-detergent oil but it says "hydraulic and compression oil" on the bottle with no combustion engine references. It's 80 degrees outside =do you think this oil is ok?
NO. Here is that oil's description from the mfr:
"Wolfs Head Hydraulic and Compressor Oil - Non-Detergent Motor Oil is a high quality mineral crankcase engine oil and general purpose oil. While modern applications are mostly in small compressor and hydraulic systems, Wolfs Head Non-Detergent Motor oil is built from high-quality mineral base stocks and may be used in crankcase engine applications wherever API SA/SB monograde oil is recommended."

SA and SB are OLD, OLD, OBSOLETE oil specs to begin with, and being non-detergent mineral base, is not appropriate at all. It is the oil used in baby oil LOL

Try the Brad Penn for the reasons stated above and then change to what you like later.

BTW, I run a lot of synthetics but don't use that for break-in. I am concerned on the rings not breaking in well with a synthetic.

Only certain grades of any oils have adequate ZDDP for flat tappet cams. You need to keep that up after break-in and through the life of the engine. Some engines with stock valve springs may do fine without the older levels of ZDDP (1200-1300 PPM) but cams with stronger valve springs are at increased risk of cam/lifter failure without adequate ZDDP levels.