Yes, I would recommend swapping out the Linksys with the TC as well. It will definitely simplify the setup of your network.
By default, the TC is configured as a wireless router so it should just work right out-of-the-box, but we still should go through some additional settings to make sure, for example, that your wireless network is secured.
Here are the basic steps ...
Time Capsule (TC) Setup w/Cable Modem
Perform a "hard" reset of the TC.
o (ref:
http://support.apple.com/kb/HT1300)
Modem/Router Power ReCycling
o Power-off the Cable modem, TC, & computer(s); Wait at least 15 minutes.
o Power-on the Cable modem; Wait at least 10 minutes.
o Power-on the TC; Wait at least 5 minutes.
o Power-on the computer(s)
Setup the TC
Either connect to the TC's wireless network or, temporarily, connect your computer directly (using an Ethernet cable) to one of the LAN ports of the TC, and then, using the AirPort Utility in Manual Mode, check these settings:
AirPort - Base Station
o Base Station Name: <whatever you wish or use the default>
o Base Station Password: (optional)
o Contact: (optional)
o Location: (optional)
o Set time automatically (optional)
o Time Zone: <select your time zone>
o Status Light: Always On (Default)
o Allow configuration over Ethernet WAN port (unchecked)
o Advertise configuration globally using Bonjour (unchecked)
AirPort - Wireless
o Wireless Mode: Create a wireless network
o Network Name: <whatever you wish or use the default>
o Allow this network to be extended (unchecked)
o Radio Mode: 802.11n (802.11b/g compatible)
o Channel: Automatic
o Wireless Security: None
AirPort - Wireless - Wireless Options
o Region: <select your region>
o Multicast Rate: 2 Mbps
o Transmit Power: 100%
o Create a closed network (unchecked)
o Use interference robustness (unchecked)
Internet - Internet Connection
o Connect Using: Ethernet
o Configure IPv4: Using DHCP
o IP Address: <provided by your ISP>
o Subnet Mask: <provided by your ISP>
o Router Address: <provided by your ISP>
o DNS Server(s): <provided by your ISP>
o Domain Name: <provided by your ISP>
o DHCP Client ID: (optional)
o Ethernet WAN Port: Automatic (Default)
o Connection Sharing: Share a public IP address
Internet - DHCP
o DHCP Range: 10.0 1.x
o DHCP Beginning Address: 10.0.1.2
o DHCP Ending Address: 10.0.1.200
o DHCP Lease: 4 hours
o DHCP Message: (optional)
o LDAP Server: (optional)
o DHCP Reservations: (optional)
Internet - NAT
o Enable default host at: (leave blank)
o Enable NAT Port Mapping Protocol (checked)
Once you have verified Internet access, I strongly suggest that you use wireless encryption (WPA or WPA2) to secure your network.