You can pretty much disregard anything that is not part of the thick multi-color wire bundle.
Some of the wires you will end up disregarding are two 24V black power input wires (Rachio has it’s own) and Red, White and Blue remote terminal wires (Rachio users WiFi & an App instead).
There also appears to be a Rain sensor involved, it has been discussed in a similar post:
To summarize, you will likely need to connect the white wire (out of the thick multi-color bundle) to one of the C terminals on your new Rachio. Than refer the image for appropriate colors (in case you wish to keep zone numbers the same) and connect zones 1 through 9 as appropriate Finally (after making sure the system works), if you wish to keep using the rain sensor (which you likely have), connect black & brown cables to S1 and SC terminals of your Rachio (as shown here).
Cheers,
Gene