When I say "angle my foot," I mean in relation to the ground. Is it best to keep your foot level throughout the stroke? Should I point my toes downward or upward at any point? I'm wondering what's best for power transfer, and for your feet and ankles.
For most people the advice goes that you keep your foot as flat as possible. There are some riders that ride toes down (even some famous ones in the Tour) but they've had a coach determine that in their specific case there is benefit to riding toes down.
It's unlikely that you can keep your foot entirely level as it comes over the top of your pedal stroke but it should be level through the power stroke and around the bottom as you pull back on the pedal to spin.
As a response to one of the other posters, be very careful about ankling. While it is touted as a great thing many coaches feel that it does nothing and is an old wives tale. Some even feel it's harmful to you. I've attached some links for futher reading on the subject.
From the reading above, and other articles on the subject, I'm inclined to recommend against it. At the very least talk to a medical professional who can look at your pedaling technique and biomechanics and advise properly.
Most hard-soled cycling shoes position your heel slightly above the ball of your foot (so a slight toes-down angle).
That's probably the angle I maintain throughout each pedal stroke, but to be honest I don't think about it much, nor do I know what's "correct". I focus on trying to make smooth circles and let my ankles do what comes naturally.
Focusing on pointing my toes down seems to help on tough spinning climbs, but it's probably just a psychological trick.