The core is best left as the gateway for the network, like I said you can disable the LMCE firewall and it becomes transparent to the user (and the DHCP works as intended).
The router you allready have (that is currently the DHCP) is then assigned as the gateway and DNS for the core.
And the DHCP server in that one needs to come off.
If you do however only have a router (from a broadband company for example) that is hellbendt on being the DHCP you need either a router after that and connect the BB router to the WAN port or, you need two NICs in the core.
There is no practical way to use a single NIC core with a router as DHCP as well.
The core usually wants to give itself the ***.***.***.01 IP, but it's easily changeable in the web-admin under 'advanced' 'network settings'.
For other IP, NIC and general fiddling work you can also use the 'advanced' 'device settings' and select 'core'
Hope this helps, but posting it time after time is ... slightly exhaustive.