Do I need to connect my router to switch, or can I connect switch directly from my modem

You can definitely have both a wired and wireless network.

Does your modem have a built-in router?  If no, then plug the switch into your Netgear router.

If your modem does have a built-in router, then you need to make a choice.  You can use modem's built-in router and reconfigure your Netgear router as an Access Point.  You can plug your switch into either the modem or router, whichever is convenient.

Or, you can use your Netgear router as a router and disable the modem's router.  Your switch should be plugged into the Netgear router.