Hi Marta,
There's a bunch of us here in the DC area and we do sometimes get together and ride... those that live close to each other more than the rest. So I'm sure you'll find someone to ride with on here.
If you're just starting out, you might be most comfortable with a flat bar road bike to get more used to things... The trek fx series is a good start. The DC craigslist has a ton of bikes on it - used. Used can usually be a great deal because lots of people buy bikes with the best of intentions and then never actually use them. Or the bike doesn't end up fitting, etc.
However, if you start of with a trek fx, it may be that later on you'll want to upgrade to something more aggressive...
I'd recommend that you go and test ride a lot of bikes... REI's a good start, but they don't always have the most knowledgable people ot help you. Revolution cycles or maybe Proteus if you're in Maryland might help.
Biking shoes, clothes, jerseys - Certain parts of your body are going to determine what type of bike shorts you want to wear. It just keeps you more comfortable in the saddle for a long time. Back pockets on jerseys gives you easy access to your stuff and its more aerodynamic... plus if you're leaning over on your bike... something in a front pocket may fall out. Bike shoes - if you're planning on clipping in, I'd start off with a set of mountain bike shoes & clips... just because they're easy to walk in.