OEM style v True style does not "require" anything, with one exception which I will mention below.
The reason why you should get adjustable arms in the back (Traction, camber, and toe arms is what they're typically called) is for your alignment tech to be able to adjust camber, caster, and toe after you change your ride height. After all, most people aren't getting coilovers to stay at stock height - if you change the height, you change the suspension geometry, which means you need an alignment.
Note that you don't just have to go to stock specs - full adjustability means you can set up your car for more aggressive types of driving. It also allows for much more aggressive wheel fitment.
Back to true v OEM style coilovers, you will need different lower arms
If you go with "true" style, you want these:
Adjustable Rear Toe Arms for the Nissan 370Z and Infiniti G37 | SPL Parts
Obviously, with the spring around the strut you do not need a spring bucket on the arm, and this eliminates it.
If you go with "oem" style, you want these:
Rear Adjustable Toe Midlinks for the 370Z and G37 | SPL Parts
Because they have a spring bucket
The lockout kit works with either. What those do is right in the name - it eliminates the adjustment from the OEM eccentric bolts that were used for camber/toe. They slip over time. If you make them "fixed" (no adjustability), you eliminate that slip. The other arms then give you adjustment in a different component in a better controlled manner.
Because our cars do not have full ad justment ability front and rear, and limited range where there is any, a full setup (from SPL because they are the best) makes a huge difference. It is expensive, sure, but opens up a massive range of possibilities to let you do things to your car
i did it to get cool wheels and look pretty in a parking lot
others did it to go faster around a track
either way, you can do everything
Your final question:
GET EVERYTHING AT ONCE. it's better to save up and get all the components (arms, coilovers). Then your shop can get the car up and throw it all on together, and do an alignment
otherwise you're looking a multiple alignments - wasted effort.
also, if u can, figure out what wheels you want to run so u can account for that as well.
i would have done it but for the massive five month wait between stuff arriving. i put the coilovers and alignment on and got a quick street alignment near stock settings with stock wheels, then when my wheels came i got a more comprehensive one where we took the time to fine tune (and also roll the fenders)