basically, changing ISP just changes the IPs, that's it. just make sure two ISPs have the exact same configurations for DNS, VPN, firewall rules, cable connections, and etc, just EXCEPT IP addresses.
however, the following considerations are recommended.
1. be aware changing DNS records might need a while to update and distribute the changes to other DNS servers. so make sure the physical switch and DNS update are in the same time window.
2. make sure the URL references used by your web server are *domain name based* (giving domain name rather than IP address in the URL) and better *relative path based* (giving a partial address - like images/logo.jpg rather than a complete address - like
www.domain.com/images/logo.jpg). this allows you to easily move a site from one server/IP/ISP to another. the same principle for access paths from the web server to other back-end services such as database and RADIUS, if applicable.
3. make sure the ports used by your web server are allowed with the new ISP. commonly, only port 80 is required. however, if your web server does use additional ports for other services (e.g. remote management), make sure the new ISP has the corresponding firewall rules in place. the same thing for the outgoing traffic from your servers, if applicable.
3. be aware that different ISPs may have different management policies for routing, firewall rules, remote access, and fault tolerance, and etc. so better make a checklist as per your internal maintenance procedures, and consult every item with the support people of the new ISP.
4. as the web service is probably critical for your business, better have a practice to estimate the required resources (time, people, and equipments) before the actual switch.
hope it helps,
bbao