280 weighs alot more then the 240Z. What all are you wanting to do? I would try to find a 240Z or a 280ZXT. 280Z/X/T will be easier to find. Both the 240Z and 280Z will be easy to work on. What engine would you use? If you get the 280ZXT I would stay with the L28ET and build on that. A NA 280ZX or 280Z and 240Z will leave more options open from an RB series motor to an SBC. Another thing is parts are more readily available for the 280 at this time. If you have to restore the 240Z to get it at a level it needs to be it might cost alittle bit more then a 280 would. Also look for a 260Z if your going to mod any of these cars will be fine. As for a Z31 that is up to you, the chasis is based off the 280Z chasis and has a few issues with rigidity (they can be fixed). The VG30ET is an amazing engine; it is easy to get power out of and very reliable while doing so. The Z31 will be a little bit harder to work on, but this car will be the easiest to find in good to excellent condition and for a very good price. Also if you pick up a 4/87-89 Turbo you will have an R200 LSD, W-series motor (better block), and a nearly indestructable engine, but they are the heaviest of the Z31s.
Handling wise the 240Z will take it if done right thanks to the light weight. All of the other cars can be made to handle well, but each time the cars got heavier. The Z31 has a weak chasis like I mentioned earlier, not enough camber in the front (can be fixed), and a trailing rear suspenion which leaves much to be desired.
If you look at a Z32TT even though this isn't the forum the possibilities are endless. The VG30DETT has problems with blocked cooling passages from the factory and the car needs cooling upgrades as you being to more heavily modify it. The suspension set-up is very good, the brakes are very good, and the engine is very good. The Z32TT has the biggest aftermarket of any of the cars you have mentioned, but they cost alot more to maintain. They also weigh a bit more, but that can be fixed. Simple bolt-ons will take this car to around 400rwhp, but after that the car gets expensive to modify.