It seems to be a popular view that Japan is wasting its money if it buys a complex before it has maxed out the first one (i.e. is transporting 8 units/turn to the mainland). However, I am of the opinion that 2 tran 1 IC–this is assuming $1 bid to Japan–is the optimal J1 purchase for getting units to the mainland quickly. There was an old thread (sorry, I couldn’t find the link on my first search and I’m too lazy to look harder) that had some calculations to this effect, but for the short version, consider:
—If you build 3 tran on J1, you can put 8 units in Asia on your second turn. However, with 2 tran 1 IC you can get 9 units there: 6 from your three transports, and three more from your complex. With a 2 IC purchase it’s down to 8 again, one from your transport and 6 from your complexes. (I’m assuming throughout that the UK killed your transport in SZ 59 so that you only have one to start with.) So if you’re trying to get as many units to Asia on J2 as you can, 2 tran 1 IC is the way to go.
—4 tran on J1, using a bid of $2, is also a good way to start fast. However, in this case your capacity outstrips your income; it will be a couple rounds before you can actually get new units fast enough to keep your transports busy. The 2 tran 1 IC buy is better optimized at keeping your production/transport capacity matched up with the number of units you can afford to produce. In particular, a 4 tran J1 purchase enables you to put as many as 10 units into Asia on J2 if you clean out Philippines, East Indies, Okinawa, and Wake, but then you run out of island units and can only make up to 8 new ones in Japan. So you get a lot of inf on J2 but it’s more of an anomaly, where the 2 tran 1 IC buy gives you a smoother and more continuous startup.
—As far as location, I like FIC the best. Kwang is farther from Moscow than either Fic or Man, so if you’re trying to put pressure on the Russians quickly you want either Fic or Man. You can supply plenty of troops to the northern area from Japan itself, so the complex is needed more on the southern end. Plus it enables you to get to Africa, Caucasus, etc better.
—So far I’ve been assuming KGF. In KJF you should certainly be a bit more hesitant about getting factories up quickly. However, I’ve found that a FIC complex, which is always where I build on J1 if I build a factory at all, can be very helpful in KJF. Ideally when defending against an American fleet you want to defend as far out as possible, e.g. with a fleet in the Caroline or even Solomon islands. However, if you’re forced to fall back, FIC is a great fallback point. The key thing about it is that it borders all three of your valuable islands. If you get in trouble you can fall back to SZ 36 and build more ships there to join your retreating fleet. Often this will be enough to prevent the Americans from taking any of those expensive islands right away. If your only factory is in Japan you’re forced to keep your navy farther north to incorporate the new builds, and the Americans have an easier time getting to the southern islands.