Hi! So, in this case you only need DNS for the f5 to resolve the name to your e-mail server. So where ever your going to send the mail out to. So your router which you use at home would work nicely. I can't remember if workstation can act as a DNS server in its own right when using nat..... Worst case, you point it at goggle, (126.96.36.199 and 188.8.131.52.) but then the f5 wont be able to resolve interally if that is a problem.
So the other question is what is the SMNP server you are going to use?