IMO fixed would not be an ideal choice for general use.
If you already have a 7 speed and are looking for simplicity, why not look for a single speed (with a freewheel, not fixed)? SS bikes are dead simple, fun to ride, and very practical if you do not have big hills (some hills are fine on a SS).

The brougham looks like a "sporty" city bike - sort of an "urban fixie"-inspired ride.

Reston is not far from DC, so you should have A TON of options not far away. Performance has a shop near you and they are having a big sale right now, so it might be worth checking out.