I think if I had to pick only one Japanese car as my favorite (not sure it's a classic) it would be an '81 Toyota Celica GT notchback coupe. You get styling that has aged reasonably well and it comes with a fairly economical engine.
Having visited Japan a few times, I'd say yes to an early model Skyline, and even better, a Skyline wagon or "commercial vehicle" (it's sort of a cross between the wagon and a panel van...a 4 door panel van?).
If I had tons of money, THE ultimate classic Japanese car is the Mazda Cosmo from the early '90s. That car had the factory 3 rotor Wankel engine (I think it may even have had turbocharging), and with it's reasonably restrained styling, it looks pretty cool. I found one about a year ago on E-Bay, the seller was Canadian...I forget what he was asking for it, but I believe it was at least $15,000.
Go to the website that HAD this car. www.silkroadautos.com Hope that's
right.
Just hoped over to silk road...they still have that Cosmo, but the engine is described as being a TWIN turbo 13B, I could have sworn the this car had the 3 rotor engine. And I was way off on the price...only $6,500. They also have a lot of other cool JDM vehicles...mostly vans and SUVs at the moment.