I lived out by Dulles Airport for about 4 years. If you know when to go, and some alternative routes, you can make it into the city and find parking with relative ease. That being said, 4th of July weekend is unique, and everything goes off the rails. For starters, most of the mall and surrounding streets are closed for the fireworks and events, and the metro will be extremely crowded, especially after the fireworks (see https://www.nps.gov/subjects/nationalmall4th/closures.htm).
Also, because it's a holiday, station parking is a bit different. I can't speak much about the red and green line (most of my knowledge is NoVA Orange and now Silver), but others are correct in that you should not count on overnight parking at the station lots. However, there is usually some parking around the station via street parking or 3rd party parking garage.
Most importantly, if there is no traffic, the metro is slower or similar to driving. Don't just stop at the head of the line to potentially avoid traffic. For example, Wiehle-Reston East to Metro Center via Metro is 45 - 65 minutes. Driving is 30 - 240 minutes. So the metro is a sure thing, but driving can be faster, or it can be way worse. Before the silver line came around, we would drive as far as East Falls Church and take the Orange line the rest of the way in.
Special 4th of July caveat
As I said, it's a zoo on the 4th. It's going terrible from every angle. Arm yourself with knowledge of the possible routes, be aware of the parking along it and near your destination, and most importantly of all; in DC, sometimes it's faster to take an extremely convoluted route than straight in.
My advise, go as far in as you can until you hit traffic, and if the beltway has no traffic, get as far south as you can, because that's where you're headed anyway!