engine out of car
 

What should I do before I install my new engine since I've got access now?

If the timing belt has around 60,000 miles on it replace it now. Install a new oil pressure sending unit. Check the water pump for a bad bearing. Replace any coolant hoses that look suspect. Fix any leaks. Replace thermostat and maybe o2 sensor.
These are things that can be done with the engine in the car but it is a lot easier to do them with the engine out. And replacing the timing belt early can save your engine. The belt is very inexpensive when compared to what will happen if it breaks. Also when changing your belt look to see if the cam seals are leaking. They are pretty easy to replace but if they leak onto your belt the oil will shorten the life of the belt.

Steering rack...
Engine mounts...
Clutch Assembly...
Is your Z a turbo? If not, think ahead (to the next project) and get that turbo cross-member in place...
Give the engine bay a complete cleaning...