On new engines, I drill prime mine while its stil on the stand with the intake and valve covers off. I can see whats going on and make sure oil is getting everywhere it needs to. After the engine is in and she is ready to go, I prime her again for a min or so, button her up and lite the fires. The only time I touch the starter is to lite her up. Dont want to spin it over on "dry" bearings. Also, when you do it on the stand, you can check your pan and lower seals for any type of leakage.
Good luck with the new engines and enjoy them.