I use Pi -> switch -> controllers. I'll plug into the switch with a computer to set up the controllers, but typically don't mess with them after that. Also have a wifi dongle in the Pi to give me access to that if needed, but I don't typically use that once it's set up. The Pi CAN act as a router in that configuration (wifi to home net, Ethernet to show net), but I've not needed it and haven't set that up.
It really depends on what you are trying to accomplish, but Pi to controller, possibly through a switch if you have more than one controller will be fine.
It helps to give the Pi internet access so it can fetch the time. So either a wifi router or a USB wifi dongle in the Pi. If you use a USB dongle, make sure the power supply for the Pi is beefy enough to handle the extra power requirements. Typical wall warts that come with the Pi don't have enough power and you get weird things going on with the Pi.
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