Are at least 2 people traveling? Inside the Beltway, I-66 is HOV-2 during weekday morning rush hour, so unless there are at least 2 of you in the car, you can't use I-66 beyond I-495.
Yes...there will be 3 of us.
Then, yes, I would recommend you go the way you described.
I see from Google Maps that they describe the route with the terms you used, but it's not entirely accurate. The road from Dulles Airport is the Dulles Access Road and is not a toll road. It's a special road available only for those going to or from IAD. Also, you will be exiting from I-66 to Route 110, not the Jefferson Davis Hwy. Route 110 will eventually lead you to Route 1 which is the Jefferson Davis Highway through Crystal City just before you get to DCA. I just don't want you looking for signs saying "Jefferson Davis Highway" when you are on I-66 because you won't see any.
Plan on this trip taking at least 60-75 minutes at that time of the morning. You will move quickly on the Dulles Access Road but you are going to be in really slow traffic on I-66 since it's rush hour.