What credit is needed for the loan rates quoted on various sites?

Simple question. I want to buy a house in January in California and I see that the rate today is 6.103% for a 30 year fixed mortgage. What FICO score correlates to those rates? My wife and I each had FICO scores of 719 and 721 six months ago. We have paid down maybe 30% of our debt. We make about $ 80,000 gross combined, have a $ 530 car payment, and are looking for a $ 300,000 mortgage with no money down.

I know that there are many factors, but what range can we expect in regards to a realistic interest rate for us?
I have $ 60,000 of available credit on credit cards to use and I have $ 6062 in credit card debt on a 0% interest card for 12 months that expires in January. I have been paying the minimum and saving the rest for when the 0% term is up rather than using the money to put down on a house.
Pay off credit card and have $ 4000 in savings or don’t pay off the card and put down $ 10,000 for the house?

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