What should I look for in clipless pedals and shoes?
Pedal Selection

Pick a system that will work well for your current and future use.  It's annoying to have different shoes for different bikes.  My experience is limited to Shimano SPDs and Crank Brothers systems -- both of these work very well for road and mountain biking.  The shoe cleat is similar for both systems and is fairly small, which means you can use it with shoes that allow recessed cleats.  Very nice to be able to get off the bike and walk like a human being rather than a duck.

If you're just starting out with clipless, definitely get double-sided pedals (some "road" pedals only clip in on one side).  If you think you might still occasionally use the bike with regular shoes, consider getting a pedal that also has a normal platform.

One other thing to keep in mind: float.  This is how much freedom your foot has to rotate.  Some folks like almost no float, others like/need plenty -- I need lots for my peculiar pedal stroke.  If in doubt, err on the side of more float, your knees will thank you.

Shoes

Like regular shoes, fit is very important so make that your first priority.  Remember that your feet swell later in the day so don't try shoes on first thing in the morning.

Also look at sole stiffness.  A completely rigid sole transfers more power, but is more awkward to walk in.  A partially rigid sole is a good choice for touring where you're not likely to pack a pair of normal walking shoes.  I have a pair of each but much prefer the rigid soles for normal riding.  Both pairs have recessed cleats.

Practice

Once you get your nifty new shoes and pedals: practice, practice, practice!  You need to be able to unclip on either side at a moment's notice.  Practice coming to a stop and unclipping -- better to get it right when you're not in traffic trying to stop at a light.  That said, you will probably still have a few falls.  It normally hurts your pride more than your body and this phase should wear off after a few months.