The T1 should be connected to your WAN port one way or another, otherwise your router cannot router Internet traffic. Nothing else should exist on the WAN port.
In short, I don't think connecting your T1 to any ports on any of your hubs will work.
Also, the "uplink" ports on hubs are usually just crossover (X) ports, but don't actually do any special routing or segregation. So whatever ports you choose shouldn't matter, aside from needing to have the right cable.
The T1 should be connected to your Linksys's WAN port, where it will handle the routing. There should probably be no exception to this. However, if you connect the new network to any of your router or hub LAN ports, they will exist on the same network and you'll have two DHCP servers (a bad thing).
With your current equipment, I see two ways around this:
- Connect the new network to yours using any LAN port you have available, use static IP address on all of the machines for at least one of the networks. Not a pretty solution and also a problem for "new" computers that hop on their network...
- Connect the new network to yours using any LAN port you have available, but do so from the secondary network's WAN port on the router. This will segregate the network from yours and their router will have to be configured to use your router as the WAN gateway.
I think the second solution is pretty reasonable.
Aside from DHCP trickery (Like a Linux server with some form of authoritative or segmented DHCP schema and MAC address bindings), I don't see any other way to solve this... I think the only "real" solution here would equipment that supports multiple VLANs, but such equipment is often very expensive and would require a holistic approach as all devices routing/switching traffic need to support QoS for VLAN'ing.