Need some guidance on transmission/flexplate/torque convertor

Hello all.
I am a little confused, getting conflicting information on my 360 magnum swap.
I bought a 1997 donor ram, have the 360 magnum engine, the flex plate, and the stock ram torque convertor.
I want to bolt this to a 1972 727 auto.
I am confused on the setup. I am being told that I need a weighted flex plate and i am good to go, or I am being told that I need a weighted torque convertor and good to go.
Now, I am being told that the ram torque convertor will not fit in the 727 (I have not tried this yet).
I assumed that because the engine, flexplate, and torque convertor all came from the same truck, i was good to just connected the 727.
Any advice?