1978 280Z barn Find / sons dream car won't stay running

[ramsesosirus]

All of the above are great places to start.   

I was your son's age when I began working on my own car:  due to not being able to afford (or trust) mechanic shops!  10+ years later, and I'm pretty darn good at it!  And I find it fun!
Accumulating tools is the hardest part.  There are lots of great resources on the internet for these cars.  They really aren't very complicated, but can seem overwhelming at first.  Mine wouldn't stay running when I bought it. 

Things to check:

pull a vacuum hose or remove oil cap while running.  The car should stumble/ or almost die.  If not=vacuum leak somewhere

clean all electrical connectors with spray electronics cleaner

check the sensors: mostly the TPS and coolant sensor.  The cold start injector can be unplugged to eliminate it.  I actually do this will all the sensors to test: unplug it and see if the problem is the same.  

After 10 years, I can almost guarantee your fuel tank is in horrible condition.  I had to have mine boiled out and the stock "pickup screen" cut out by a radiator shop (you can't always do ALL of your own work, but it is a balance...)  Mine would run for a few minutes, then die like yours...

Having the tank professionally cleaned, adding an extra fuel filter, new fuel pump, and cleaning electrical connectors fixed mine.

I would advise your son to become mechanically inclined.   Almost no one is going to be able to afford to take these cars to a shop everytime.  They really aren't that complicated.  

And I commend your son on getting his "dream car".  I bet he can figure it out, and it will give him a great feeling (and a great skill) to start doing some of his own work.

Safety first though, jacks, jackstands, fuel safety, glasses, e brakes, chocking the wheels, etc....