DNS Configuration question

I recently had an issue with my workstations not being able to get online.  The problem was that they could not find the DNS server.  I called my ISP (Charter), and they reset everything.  The end result is that if I use my old router (Linksys) everything works fine.  If I try to use UTM as DHCP, only some of my workstations are allowed access.  The others have the ability to connect to my network, but not the internet, or the UTM GUI.  The settings on one of the workstations is:

static IP:  192.168.1.136

subnet:  255.255.255.0

gateway:  192.168.1.1

primary DNS:  71.10.216.1

alternateDNS:  71.10.216.2

My question is this:  Do I still use Google DNS settings for the UTM per the Best Practices?  If so, do I leave Charter's DNS settings on the workstations, or do I have to use Google there as well?  I currently have Charter's DNS settings in the UTM, which clearly is wrong.

Thank You