Some thoughts on the IJN Carrier force...
KB
I discovered (probably forgot a long time ago) that I can't change the size of the air units on the fleet carriers. I think that I will be able to change them to what I want after they can change historically, which is July 42. (The CVLs and CVEs can change from day one, and I did that.)
So, how do I set up the air groups? Typically, I'll make the fighter group around half the max for the carrier, the torpedo bombers will be about a third of the torpedo complement and the rest will be dive bombers. Here's what the air complements will look like come July 42:
Ship - Zero/Val/Kate
Akagi - 39/27/15 - 45 torpedoes (81 plane capacity)
Kaga - 39/27/15 - 45 torpedoes (81 plane capacity)
Hiryu - 36/15/12 - 36 torpedoes (63 plane capacity)
Soryu - 36/15/12 - 36 torpedoes (63 plane capacity)
Shokaku - 36/21/15 - 45 torpedoes (72 plane capacity)
Zuikaku - 36/21/15 - 45 torpedoes (72 plane capacity)
So, come July 42, KB has a total of 222 Zeros, 126 Vals and 84 Kates. That's not a lot of Kates, but they use torpedoes pretty much exclusively.
I give each daitai 3 spare planes and 3 spare pilots. It gives them a little staying power in case things get ugly.
Just about all the time, I'll keep 10% of the Kates on naval search, so those 84 Kates are effectively 76 Kates.
I usually keep the carrier divisions the same as was done historically. I like to put them in TFs of about 200 or so aircraft when I anticipate combat and will divide them up in 2 TFs, with Akagi, Kaga and Hiryu in one and the other 3 in the other.
Almost all the time the fighters are set on escort with 60% CAP. So, if full air loads fly, they are escorted by about 89 Zeros with about 133 Zeros flying CAP over the carriers. I set the Zeros and Kates at range 7 and the Vals at range 6. The Vals only carry 2x 60 kg bombs at range 7, which is pretty useless. I always try for combat within 6 hexes so my attack force is increased by about 150% with the addition of the Vals.
Later in the war, I'll use a mix of A6M3a for long range escort and A6M5c (armored) for CAP. By that time I have the Judy III/IV and the Jill, which greatly increases my attack range.
MKB
All the little carriers are MKB, which currently is Ryujo, Shoho, Zuiho and Hosho. Taiyo will eventually be added once I get some Val pilots trained up. Here's their composition:
Ryujo - 36/0/12 - 27 torpedoes (48 plane capacity)
Shoho - 21/0/9 - 18 torpedoes (30 plane capacity)
Zuiho - 21/0/9 - 18 torpedoes (30 plane capacity)
Hosho - 14/0/6 - 6 torpedoes (20 plane capacity)
Something I learned about Ryujo. She sucks. She's blessed with a large torpedo capacity but has only 141 sorties. Even little Hosho has 220 sorties.
Right now, I keep them all together, except when Ryujo has to head back to port to replenish her sorties.

They are really fragile, so I keep them out of harms way for the most part. They stay out of the big girl battles. Sometimes, I'll keep MKB in the wings of a large battle to help with clean up should things go wildly in my favor.
MKB tends to spend a lot of time in the SRA, where they can ambush TFs heading from the Indian AO to the west coast of Australia. I remember last game, I caught a big convoy hauling 9 Australian Division and utterly destroyed it. I think only 1 or 2 beat up xAPs survived. It was glorious for my little MKB.
Carrier Reinforcements
I'm kind of weird about this.
I shut off Shinano. Nuff said.
I currently have Hiyo accelerated. She 77 days out. Junyo is 65 days out. When Hiyo reaches Junyo (in 12 days) I'll set her to normal so they both arrive on the same day. They will be the same CV Division and will steam together. They're really slow (25 kts) so they are the flagships of MKB.
Ryujo comes out on its normal date of 28 Nov 42. Her air complement doesn't arrive unit 1 Nov 43, so she'll most likely sit in port unless I lose a carrier, in which case she'll pick up that carrier's air complement. I may give her some land based planes, but I like to keep all I can training. It all depends on the situation.
Taiho is a nice ship, but expensive. I keep her building normally, but I'll accelerate her later when my other carrier (see below) are built. I anticipate getting Taiho around the end of 43.
Amagi, Unryu and Katsuragi are a carrier division (189 total planes) and I am currently accelerating them until they are all arriving on the same date. Right now the first 2 are arriving on 24 Jul 44 and the last is accelerated and is currently at 30 Aug 44. By the time she meets the other two, I'll be able to accelerate all 3 at the same time. I should get them in late 43.
CVL Ibuki will accelerate later and arrive probably in mid-44. We'll see...
The last 3 CVs, Kasagi, Ikoma and Aso are also a carrier division and will be accelerated together like the other 3. I anticipate them arriving in early 44.
Other ships
I am building Yamato and Musashi, which will arrive in 82 days and 1 Dec 42 respectively. Once they're done, that'll allow me to accelerate more carriers. Can't wait.
I accelerate all DDs, as soon as I can. Right now, it's only 7 but I'll accelerate as soon as they are able.
I'm getting the CLs as they come.
I'm building the subs as they come. I stopped 57 and have 104 still coming.
On the merchant side....
I'm accelerating CVEs Unyo (8 days) and Chuyo and am allowing Kaiyo and Shinyo to arrive normally. These guys will most likely provide naval search and ASW support to large convoys.
I currently have 8x Type-1 TM class TKs (8150, 14 kt) accelerated (2 have arrived). I'll probably accelerate more as time goes on.
There's lots more, but I already babbled on more than I wanted to.