Setting up TimeCapsule with existing Router(with DHCP disabled) I have an existing Belkin modem-router, and a new Time Capsule. I would like the Time Capsule to act as the router and DHCP server, and the belkin modem-router to just be a modem.

I connected one of the LAN ports on my Belkin Router to the WAN port on the Time Capsule and then disabled the DHCP server on the Belkin Router.

Now when I set up the Time Capsule I'm not sure what settings to choose?
On Manual Setup on the Internet tab, should I choose share a public IP address or Distribute a range of IP addresses or bridge Mode? It is also asking for settings like DNS server? Surely the WAN IP and DNS Servers should be handled by the modem?

And In the internet tab, under TCP/IP should I choose Manually or DHCP.

Basically I want my Belkin router to be only a modem, and the Time Capsule to do the DHCP, NAT, Wireless, etc.
Disable NAT and DHCP on the router.  Plug the Time Capsule's WAN port into the router's LAN port.  Better yet, see if the router has a "bridge" mode.  The Time Capsule usually would run in 'distribute a range' mode, which IIRC means DHCP and NAT.  'Share a public' would be DHCP only.  And bridge is a simple pass-through mode (much like we've just tried to put your Belkin into).