How necessary is a static IP when running a webserver from home
Solution 1:
It is not necessary to have a static IP to run a webserver from home as long as there is a static name in DNS that will update if your IP happens to change.
This is possible through a variety of DNS providers. Dyndns and No-IP are probably the most well-known providers. Another DNS provider, EveryDNS (which is now owned by Dyn), also provides this service.
Additionally, if you are using a router like the linksys wrt54g that allows you to put an open firmware on it (like tomato or dd-WRT) you can often automate the updating of the IP address with the dynamic provider so that when the router gets a new address from DHCP, it will automatically update with your dynamic naming provider.
You should also check your terms of service for your residential service. While this is technically possible, running a commercial website from your home is likely to be prohibited by your ISP.
Solution 2:
You could use www.dyndns.com to monitor your dynamic ip and change the dns records automatically. I've used it for simple setups and it works well.
But, a home internet connection might not be the best solution for a reliable 24/7 software service that always needs to be available.
Solution 3:
Some of the content will be software that need to run reliably 24/7.
Don't run it from home, then.