you are correct in saying to use a mineral oil for initial running in, can help prevent glazing of the bores when using new rings e.t.c
i always initially start up an engine with no coolant for about 30 seconds to get some heat in the head gasket.
crank engine with no spark plugs in till oil light goes out.
when an engine is assemled you should use an assembly lube of all connecting surfaces, bearings, and use plenty of cam lube on camshafts and followers e.t.c

the running in time is greatly over exagerated by many people, a crank is machined to tolerances that dont require running in, camshafts just require about 20/30 at about 2500, NEVER let an engine idle on new camshafts cause the oil pressure is lower at idle.

once run for 30 seconds fill system with appropriate amount of anti-freeze and water, check oil level and tension of all running belts, especially cam belt.

then i do 50miles or an hour driving use 50% revs, 3500rpm ish. then a trip to rolling road to get mixture/timing checked e.t.c and then providing all is well you can then use the engine to its full potential.