The untagged/tagged part of this is confusing, it took me some time playing with it to really understand it as well. But look at it this way. Each VLAN has to have its own default gateway to get out to. In some high-end routers, you can have sub-interfaces all assigned to a single physical interface, so one ethernet port on the switch is considered three, four, or more virtual ethernet ports, each one being a default gateway for one of the VLANs. In this situation, you'd have to use a trunk port from the switch to the router, or a TAGGED port, which would send all of the VLAN traffic through a single line to the router, tagged with the number of the VLAN that traffic is coming from, to get to the right default gateway.
Now, in most situations you're not going to have a router that can do multiple sub-interfaces on a single physical interface. Instead, you're going to have a device like what you've got where you can assign only a single address or physical network to a single physical interface. That means that one physical interface can only be the connection for one VLAN default gateway. In that case, you don't need a trunk port, it's going to be considered an access port, or UNTAGGED port, just like any others on the switch. You want all the computers in that VLAN to get to the proper default gateway, so the router which has the proper default gateway address must be UNTAGGED for that VLAN to pass data out to the IP address. No other VLANs are passing traffic along that interface. The other VLANs will have to pass traffic to their own router and interface directly.
Obviously if you have many VLANs, this gets to be prohibitive which is why the have high end routers capable of multiple sub-interfaces on a single physical interfaces.