If you go with my suggestion, there's no modem to manage so it doesn't matter that modem-manager does not work
Instructions for using the GUI to set up an automatic network configuration, equivalent to what your Vista system was probably doing, are here
. You want Ethernet and DHCP. There doesn't seem to be a way to automatically set DNS server names so you need to set your ISP's. If you don't know those you can use public DNS servers from Level 3 (184.108.40.206 to 220.127.116.11) or OpenDNS (18.104.22.168 and 22.214.171.124). The latter show advertising when you try to browse a site that does not exist.
EDIT: or you could set the ZyXEL as DNS server. Once automatic network configuration is working the ZyXEL's IP address will be shown in the output from root -n