I do:

extractor->silo->factories (P1)->launchpad

I tend to try to keep my silos 1/2 to 3/4 full of product, keeps me from having to move heads, and if I miss a day I don't always empty out the silo since silos hold considerably more PI than the command center (I never link the command center to anything)

you can do an expedited transfer from a silo to a launch pad or vice versa I do this sometimes when I have to move extractor heads far away from my base.

for my robotics setup its 4 extraction planets, 1 factory planet (P2 and P3)

You shouldn't go from factory to factory, buffer it with some sort of storage like silos or launch pad. You can't create routes between storage faculties. You can create a route that spans multiple links. So always route productto storage and then to the next factory.

Personally I believe there are 2 ways to run PI. The lazy way and the hard way. (Lazy, I choose you. )

The lazy way is to produce P2 on each planet and leave it at that (maybe 1 Factory planet for multiple accounts or P3 products) . Each planet has 2 Extractors , and Factories to produce the P2 parts. I personally use 3 of each (3 Basics for each P1 and 3 Advanced to product P2) , then its just a matter of finding a balance between the two P0 extraction .

Extractor -> Launch Pad -> Basic Factory -> Launch Pad -> Advanced Factory-> Launch Pad

This limits the amount of work you have yo do. Very little PI moving, Very compact product , No expediting . With the 3X3 set-up I run you can get 300+ P2 units per planet per day.

The not lazy method is to produce P1 and move that to Factory planets. Even a bad planet will fill a launch pad in 3 days with 6+ basic factories. Then you just need a tonne of Silos, Factories and Launch pads on the factory planet to taste.

Extractor -> Launch Pad -> Basic Factory -> Launch Pad

You can go from factory to factory if you go from a basic to an advanced. The basic has a 30 minute cycle time and the advanced 60 minute. The advances needs 40 input and basic outputs 20. So every 2 cycles of a basic = 1 advanced. After 4 cycles your advanced will always be producing and have a full hopper for the next cycle. Assuming your basic doesn't stop that is.

The problem with that is if the advanced factory buffer is full and the basic finishes first then you lose those basic factory products, especially an issue if one raw material is in excess of another. Factories can also get out of sync by the nature in which they move raw materials and products.

Extractor -> Launchpad -> Basic Industry -> Adv Industry -> Adv Industry -> Launchpad

Better to just route everything through the launchpad:
Extractor -> Launchpad -> Basic Industry -> Launchpad -> Adv Industry -> Launchpad -> Adv Industry -> Launchpad

That way you've got a buffer to hold any overage if you're not in balance.

I've recently been using a multiple planet setup. I have 5 planets per character (2 characters atm), 2 are factory planets, 3 are extraction planets. I'm in nosec, so the outputs are much greater than hi/losec.

On the factory planets, I use 3 spaceports, 6 adv factories, and 12 basic. Two of the spaceports hold P0 (one for each type used) and the third handles all P1 and P2 materials, plus a little extra P0 as buffer if I don't log on in time to refill everything.

The extraction planets are 2 sets of 1 extractor and 1 spaceport (4 facilities total). They chase hotspots and at 945000 ISK, they are cheaply replaced if I move to a new hotspot.

To start things off, I extracted for a weekend to build up an initial supply of P0. Then I built the factories and fed them the P0. I let it go over night to build a P1 stockpile. Then I cranked up the advanced factories. This leaves me with a buffer of a few hours worth of P1 materials if I don't log in at the right time. I stayed on top of the extraction for 3 weeks (i'm in week 4 now) to maximize my stockpile of P0. Once I've got a good buffer supply of P0, I'll give the extraction planets longer run times (e.g. a week or two) to slowly backfill the reserves at about the daily rate of factory planet consumption, but without the daily extraction upkeep. I've currently built up about a 14-day buffer for 24 adv processors. Once I have command center 5 (next week), I can increase the amount of materials stored on the factory planets so that I only have to refill things once every two days. I expect to reach the point where my total time spent maintaining the operation will be around 2 or 3 hrs a week max, spread out over many days.

Just another way to do it. Trying to do everything on a single planet leaves you in the position of having to worry about equilibrium and all that jazz. This method gets you past the point of needing to deal with equilibrium at all.

I agree lazy all the way, but I also want max efficiency =\ with 3 basic and 3 advanced that leaves open too many cycles not producing anything. You could get away with 2 basic and 2 advanced which frees up more cpu/pg for more extractors. I also use my launchpad as a main hub, but I don't know how to incorporate silo storages for resource/product overflow/holding. I was thinking about Extractor -> Silo -> Basic Factory (P1) -> Silo -> Command Center (don't know if this counts as a storage) -> Launchpad. I haven't had a chance to try it out but doesn't that technically break the storage to storage limit and still stay within the 6 routes maximum?