Weather wise, sort of like the U.K. Cold & Damp. Chance of rain & snow. Check the Dulles International Airport website. You will find Washington Flyer information (taxi, bus &shuttle info) I think they have an exclusive contract to provide transportation from Dulles but am not certain. Check their website. Have a good trip.
This hotel is about a 30 minute drive from Dulles Airport. Taxi fare ranges from $50 to $70 depending on how bad the traffic is. Super Shuttle would be a cheaper option if it goes to Manassas-area hotels. (I don't know if they do.)
But once you get to your hotel, you will likely need a car anyway to get around Manassas It might be a good idea to just rent a car at Dulles.
Keep in mind that there are federal holidays in January that impact what businesses/attractions are open and how public transportation works. For example, if you are planning to use the VRE or bus service to DC, they are either not working on these days or on a limited holiday schedule.
Monday, January 2
Monday, January 16
And then on Friday, January 20 - specific to the Washington, DC area - Inauguration Day. Public transportation will be working on a special schedule and it will be a zoo trying to get into DC and around the immediate DC area.
Days around Inauguration will indeed be a gridlock.