Getting Transmission Rebuilt

I was thinking about removing and installing it to save money. We have a lift, so, I was thinking about getting a transmission jack.

If I were to do this on the lift, what would be the best steps?

Unbolt uppers then lift the car up and unbolt the lower ones? Will the engine want to tilt back a lot since the tranny isn't supporting it? Someone mentioned putting a strap from the front to hold the engine from tilting back.

Would I need to remove and unbolt that large crossmember support near the back of the transmission to get it out?

Thanks for all the help on this