The one address you actually do care about is that of the server you mentioned. If the server is behind the NAT, you have a configuration on the Linksys that translates a certain set of TCP and UDP port numbers when addressed to the Linksys to the interior address of the server, and when you change ISPs you will have to change that configuration. Frankly, while the task is different, I don't see a large workload difference between changing that configuration and changing a similar configuration that poked an incoming hole for web and mail traffic to your web and mail servers.
Did I mention Dynamic DNS? If your server is capable of interacting with your DNS server (that's a question, some are and some aren't), Dynamic DNS can eliminate the need to concern yourself with the server address.
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