I might be able to pass you a few bits of helpful information. Although it might just sound like common sense.
---There are a lot of export companies in that ship skylines and other cars to the US and all around the world. They are extremely good at it and know the laws and paperwork needed, i highly doubt they'll mind if you come to see the car before you buy it, it'd help to call them first though, don't take my word. Search googles for some of those exporters. Plan your flight to the location of the export that you think best fits you. If you buy from a used car dealer or an ad, then you are still going to need the help from an exporter.
---The cars are 25 years old, so you will find something wrong with all of them. Japanese owners mostly modded them and did basic upgrades, you're going to find that on basically all of them. An important thing to watch out for is an aftermarket japanese ecu. good luck finding someone in the states that can tune it. But getting there and seeing one is going to be a big advantage to someone buying blind (like me). You'll get to check those wear parts like you mentioned, but most of the parts you'd be buying are going to be expensive there too, so you wont save much money and might lose some depending on conversion from dollar to yen. Additionally you need find suppliers in the us or online where you purchase parts anyways, the car is 25+ years old and things are going to break/fail.
---Once you find your car, the exporter should get you all set up with paperwork. But you won't get all of the paperwork until the car is ship. So you'll end up leaving japan before you car does minus the money you spent on the car. It'll be a bad feeling, but japanese companies are quite trust worthy. Once the car gets to the US you'll need a customs agent to get all your payments for dutys tarifs and whatnots. depending on which state you register the car you'll be pay X amount in taxes. You said you've got the funds for this, I estimate you'll spend 18 to 22K on the car, 2k to ship, 1 to 3K in taxes. not counting the cost of your trip, which could be 2k to 2m (japan is expensive!).
---While you are in japan enjoy some ramen, gyouza, sushi, and pachinko (if you like smoking, loud noises, and gamb|ing for metal balls). Get over to see Kyoto or Fuji if your location permits, go when the sakura trees are blooms in the region you go to (you'll thank me..). You might as well see as much of Japan as you can since you are flying over the pacific.
Hope that helps a bit, it's nothing solid, like do this to get that, because there really is no set way you have to go about it.
source: i was stationed over there for 5 years, i've imported a 91' Gtr recently.