Any modern gear system sold on the sorts of bikes you'll see in a bike shop will work just fine for a casual rider. Better (more expensive) gear systems might shift just a little faster, and have components that weigh a bit less. The only thing I might suggest is staying away from the very cheapest, as some of them tend to need more frequent adjustment. But probably the Smoke and Dew are both fine in that regard.

More vs. less gears is a preference. The bikes you will probably be looking at will have either 8 or 9 gears in the rear, which is more than enough. The only thing you might think about is whether you want 2 or 3 gears in the front. The tradeoff is that 2 gears in front is easier to maintain and is less complicated, but having 3 gears lets you have a "granny gear" for helping you get up big hills. For the most part, newer riders see benefit in having the granny gear, and the DC area has enough hills that I like having a granny gear on my bikes.

For what it's worth, you can take a regular bike on the Metro outside of peak hours.

Good luck, and have fun riding in DC!