While one could supposedly create stop motion animation using off-the-shelf action figures, those are sadly very difficult to work with. Even modified to add tie-downs, you'd still find that they are generally not balanced properly (being very top heavy they'll have a tendency to topple over), and that their joints were not designed for precise movement in small increments. This means that if you want to obtain decent results, you'll generally want to create your own stop motion specific puppets.
An ideal stop motion puppet should have a number of qualities which you would appreciate when animating it. First, the whole puppet should be as light as possible, and balanced so that its stance is neutral (i.e. it doesn't have a tendency to topple to any one side). Keep in mind that in order to animate the puppet, something will need to keep it pinned (generally a tie-down or rigging system) while you would be repeatedly moving some part of it in small increments. The heavier the puppet, the harder it is to keep perfectly pinned, and the more resistance will be encountered when trying to move a part of it.
Imagine that your character is a humanoid standing upright, and you want to animate it waving its hand. In order to accomplish this, you will need to move the hand without moving the rest of the body. If the body moves even one millimetre during one frame, it will look bad in the final animation. Also, the movement of the hand needs to be done in very small increments (which for a 30 cm puppet would mean a few millimetres at a time). If the puppet's hand is very heavy or stiff, it will try to resist your push/pull; this means that you will need to apply more force, which in turn increases the chance of accidentally moving the whole puppet, or of overshooting the motion of the hand. So you really want that hand to be light, and to move smoothly.
On the other hand, though, you don't want the puppet to move by itself between shots. So while the joints should allow smooth movement, they should nonetheless be stiff enough to maintain - indefinitely - the position you left them in. This is why the skeleton of the puppet - its armature, as it's called - plays such an important role, and why I will dedicate an entire section to it.
Of course, the skeleton is not the only factor affecting a puppet's movement. Like you, the puppet will likely have the equivalent of muscles, flesh, skin, and clothing, all of which can interfere with your animation. Tight pants can restrict movement; thin skin can break after repeated strain; elastic muscles can resist motion, and so on. I will address some of these issues in the body buildup section, but the main thing to keep in mind at this point is that every choice you make in the creation of a puppet will affect your ability to animate it.
The design of the puppet is therefore critical to your success at the animation stage. So while you might initially think that covering a raven puppet with real feathers will make it look cool - and it will - you'll later find that it is a nightmare to animate. The feathers will get ruffled in every frame - you don't even need to touch the puppet, just breathe close to it - making the final animation look like it was shot in blizzard conditions.
Sadly, though, not all of these problems can be anticipated at the design stage. And yet, stop motion is so immensely time consuming that you really can't afford to have your puppet break half-way through shooting your short, after months of animation. But there is one thing you can do to help your odds: prototype.
Before starting work on any of the actors you see in A Shroud of Silence, I made a complete puppet which was used solely as a prototype. This allowed me to experiment with different fabrication ideas on something which I wasn't afraid of losing (since I knew from the start that I won't be using it in the short). This extra effort was more than worth it in the long run, and I strongly recommend taking the time to do it.