If the car is new to you and you are unsure of the past service history then I would advise getting a 60,000 mile service completed by a recommended 350Z Indy specialist.
The drive belt should be replaced if showing signs of wear or is past the self adjusting maximum mark.
The spark plugs should be replaced if the gap exceeds 0.055in.
The diff fluid change is straight forward and should be changed depending on the past driving conditions.
Have a look at the Nissan service intervals etc below.
https://www.nissan-cdn.net/content/dam/Nissan/za/Maintenance/370Z.pdf