just want to verify that if we want to connect a server to a Cisco switchport, do we configure the switchport as access or trunk?
Modern day server NIC's are capable of running 802.1q on their NIC. Put simply this means the server can form a trunk with the switch. So the server can be a member of multiple vlans and send traffic for all vlans at L2 across the trunk link.
This is seen quite often with VMWare servers where multiple virtual servers are each in different vlans but obviously you only have one physical NIC on the server.