DC is a good biking city.
Traffic can be heavy, but once you learn the routes you can find the low traffic alternates.
Some road conditions can be iffy (lots of new construction and infrastructure rebuilding), but most are fine.
Lots of excellent trails and mup's along with the roads.
Sidewalk riding is allowed outside of the central business district, but I seldom see the need to use them. The roads a generally safer and in better shape.
Generally flat terrain with short, steep hills as you climb out of the river valley.
Lots of people bike commute. I wish I could (car needed for work almost every day)
I know a few people living in the city or inner burbs who get anywhere they need to by bike, walking and/or Metro.
(btw - bike are allowed on Metro at non-peak times)

As for leaving a bike out overnight, I probably wouldn't unless it was really cheap, and never unlocked.
Daytime parking would depend on the neighborhood, where and how it was locked. I often lock up for a couple of hours and (almost) never have had a problem.
Type of bike is your preference, but for commuting I'd recommend something sturdy with good tires.