First time motor pull

Yes drop the engine in put the car up on the lift and bolt the tranny in from underneath. No running involved in till the engine and trans are in. The engine goes in easier with out the tranny hanging off the back.
Not in my 30 years of pulling and installing. I would much rather pull and drop as a unit. So much easier than fighting the trans trying to shove it up in there with the engine dangling by the mounts. But whatever floats your boat