In another thread I was asked about rinko, so I thought I'd start a new thread about it.
Here is a picture of my Homer in rinko state:
(In the plastic bag are brake cables, headset nuts and spacers, and pedals)
And my Hunqapillar (taken several years ago but basically same now) :

I always pack my bike as small as possible when rinko'ing, removing fork and rear wheel from frame, but to be honest, I'm a minority. Most people just remove wheel(s) from frame and that's it.
I'd suggest that you pack your bike as small as possible, especially if you are not familiar with trains in Japan, for several reasons:
(1) Most railway companies do not allow bikes with only one wheel removed. To be accurate, sum of three sides must be smaller than 250cm, and bike with one wheel removed exceeds this size. (Although, in most cases, station/train staffs just let you get on the train)
(2) Trains in Japan is often very crowded, and you might have a hard time getting on, especially when carrying a big baggage.
(3) Even long-distance trains have poor baggage space if any.
(4) Compactly packed baggage is easier to carry than big baggage, if both are of same weight. Big stations such as Shinjuku, Shibuya, or Umeda, are like mazes and are often referred to as "dungeons". You won't want to wander such places with big baggage on your shoulder.
As for bikes and tools...
Brakes : Cantilever, V, or Centerpull. You can pack a bike with sidepull brakes, but there's more hassle.
Headset : Rinko specific headset is ideal I guess, although I've never used one. My bikes have ordinary cartridge-bearing headsets. Cup-and-cone headsets, needless to say, add hassle.
Handlebars : Simple straight bars or not-so-wide drops are easier to pack. Boscos are very difficult to pack.
Pedals : Quick-release pedals, such as
MKS's Ezy-Superior pedals, are recommended.
Tools and accesories :
Apart from tools which you regularly carry, you would need 32mm headset wrench(es). I used to carry two, but after I swapped front brake cable hanger to Rene Herse's, I noticed that I need only one. (Rene Herse's hanger fits very tightly, preventing lower nut from rotating)
Frame pads to protect paint (you can use towel or rag instead).
Rear-end protector (pictured in 02
here)
May or may not be necessary depending on your rear derailleur and your rear rack.
There are some more to add, but that's it for now.
Takashi