I have this modem/router/gateway that is aid to have a 4 port gigabit ethernet router. Since this is a router, can I go straight to a switch in my wiring closet or do I need another router in between?

ARRIS SURFboard SBG7580AC Docsis 3.0 Cable Modem/ Wi-Fi AC1750 Router

It says its a router, but everything you read online says go modem to router to switch, but what if you have a combo device?

Straight from the Arris to your switch is fine.

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everything you read online says go modem to router to switch, but what if you have a combo device

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ONE router is sufficient. As long as the switch is plugged into the router, it is fine. All a combo modem/router does is cut out the need for an additional router to be hooked into the modem. The router hands out IP addresses over both ethernet and wireless if it is so equipped. The switch just works like a power strip -- provides extra plug-ins for ethernet cables.

thanks guys