Years ago, the software travel agents used for checking flights was made public, and I use that to check flights. It doesn't sell flights, so it is non-partial. It also covers some airlines 3rd party booking sites don't cover.
As you have a little flex time, you can set it to look a day or two before and after your travel dates of consideration.....and to look at airlines within a distance of Dulles.
It can be googled by Matrix Air, but it has also been replaced by Google Flights as mentioned above. I just like the old version, myself.
If you have a little time before booking, consider looking for a flight of interest. There are other websites where you can set notifications for price drops....or sign up for that airline's emails for sales.
A caveat is that there is no such thing as a 'best' for everyone and everything. Each needs to make a decision of what is their priority. Some will fly all over God's green earth to save $100, others pay for the convenience of a direct flight.