Here's my situation. I have broadband connection via cable, I connect to the internet via DHCP. Do I need a static IP address from my provider? Are there any additional fees that providers charge for typical VPN capabilities? Any other issues I need to coordinate with my cable provider?
No you do not need a static IP from your provider. Though having one may make whatever random activity you are planning easier. (You never said why you are asking this question so without context my answer also has no meaning to your purpose)
No you do not need to pay any additional fees unless you want to.
No you do not need to coordinate with your provider unless you want to.
I can only assume that you have some intended use of VPN technology in mind when you posted but I cannot tell if you want to run a VPN server or client. I cannot tell which VPN technology you plan to use, and I cannot tell which implementation of that technology you are considering.
Now if you would care to elaborate on exactly what you are planning then the answers may change. Some VPN servers can operate with a dynamic IP using a dynamic DNS service to map a hostname to your current IP address and avoid paying for a static IP.
I'm assuming that you can pick any VPN technology and even if your provider is blocking certain ports or doing some traffic shaping that throws certain VPN packets in the bit bucket you can change to something else.
I'm also assuming that you are not running a server so you would not have any problems with the terms of service of your provider for running a server on your end.
Now if you are running a server, a static IP is helpful. If your provider has terms of service that forbid running a server on your class of connection then you may need to upgrade or you will be breaking your service agreement and may loose your connection. Also if your cable ISP is like my cable ISP they do traffic shaping on all their connections unless you pay an extra fee for static IP and a dubiously named quality of service add on. Running a server on a static IP is better than on dynamic IP's because then you do not rely on a dynamic DNS service and client software to be working. I have many clients who use a dynamic IP for their VPN server because it's not critical but there have been many times where the dynamic DNS client stopped working or their dynamic DNS service account sent an email notice that required them to click on a link to renew the account and they didn't do this so the account expires.