If you have decided to build your own puppets, then the very first thing to consider is what kind of armature (skeleton) to use for it. This choice will influence a number of other elements, including the overall size of the puppet. A good size for humanoid stop motion puppets is around 30 cm (or 12 inches), which is just large enough to not require infinitesimally small motion increments, while keeping the scale of your sets manageable inside your average apartment room (unless, of course, you live in Japan). If you are purchasing an armature, however, then pricing and availability might play a role in deciding the scale.
While one could conceivably build a poseable skeleton in any number of ways, the two most common choices are wire, and ball-and-socket armatures. Professionals tend to use the latter, but this doesn't mean that the former is a bad choice; it just won't be as good.
WIRE ARMATURES
Wire armatures are the cheapest and simplest to make, as the fabrication process is literally no more complex than twisting some wire into a stick figure shape. The resulting poseability, however, depends to a large extent on the mechanical properties of the wire you use, and this is unfortunate because metal fatigue will cause these to degrade over time.
The idea of wire armatures is simple: after bending, wire tends to maintain that pose (which is what you want for stop motion animation). The first thing to keep in mind, however, is that different wire types will exhibit different degrees of elasticity: some are more springy than others, and will want to fight your changes by springing back to their initial pose. The common gardening wire which you can find at the hardware store is likely to be very elastic, making it a poor choice for animation. What you'll need for your armatures is aluminium wire. This bends very smoothly, and has very little springiness.
The other thing to keep in mind about wire is that repeated bending will cause it to wear down and eventually break. This is one of the reasons why you never want to have a single strand of wire in any part of your armature; rather try to always use multiple thinner strands twisted together. This will prolong the life of your armature, but do keep in mind that it will only be delaying the inevitable. The number of strands and how tight they are twisted together will affect how much longer they last, but it will also affect your ability to animate it. Too many and you'll have a hard time bending them; too few, and soon enough they'll become too loose to even support the pose of the puppet.
The thickness and number of strands in your armature are therefore variables which you will need to consider based on the needs of your project. This is one area where building prototypes is very important, as it can save a lot of frustration later on. As a rule of thumb, though, take a look at your shot-by-shot breakdown and try to imagine what kind of - and how much - movement your puppet will need to do. Any part which doesn't require fine movement can (and probably should) be made more rigid. If, for example, you don't expect to show your puppet's feet in motion, then make them very sturdy; or rather "extremely sturdy" as a puppet's legs and feet need to be very sturdy to begin with. Unlike hands, the feet need to support the weight of the puppet, and will generally see the most stress. This is especially true if you are using tie-downs in the feet, because this means that any force you apply to a part of the puppet will at least partly be transferred to the feet. And you really want to avoid the situation where your puppet can no longer stand up because its knees just buckle up every time you touch it.
No matter how thoughtful you are regarding the puppet's design, though, working with wire armatures will always be a race against time. They will inevitably break down, but there are a few things you can do to maximize the chances of finishing your short before this happens.
First: be diligent about planning your animation. Every re-take increases the wear on your puppet, so try to minimize these by getting things right from the start.
Second: avoid unnecessary strain on joints by using supports. If your puppet is currently holding a pose which would make a yoga master cringe, and you are considering having tea before the next shot, try to prop up the puppet in the mean-time, using whatever improvised supports you can make or find. Imagine that it's a real actor, and that the more tired it becomes, the worse off you'll be in the long run.
BALL-AND-SOCKET ARMATURES
As the name would suggest, ball-and-socket armatures rely on the idea of a metal ball being sandwiched between metal plates. The friction between the plates and the ball can be controlled by tightening or loosening a screw which keeps the plates connected.
Being able to control how loose a joint is gives ball-and-socket armatures a huge advantage over their wire counterparts. Whereas the latter can only be "configured" in the initial building stages (by using different thickness and tightness-of-winding to define how loose a joint will be), the former can be adjusted at any time. And this is great not just for convenience, but because it essentially does away with the main problem of wire armatures: wear. As you keep bending the wire, it will become more and more loose (until it breaks altogether), and there's really not much you can do about this. But when a ball-and-socket joint gets too lose, you can just tighten it up again. So the puppet's skeleton would no longer affect its durability.
Of course, having adjustable joints does bring with it some complications, in that in order to take advantage of this, you will need to maintain access to the screws which control them. So you can't just bury the skeleton - you'll need to leave some holes in the puppet's body, and probably cover them up somehow (if you don't want them showing). You'll therefore need to spend a bit more time planning the puppet's body and costume.
One other thing to consider about ball-and-socket armatures is their similarity to a human skeleton: they are comprised of rigid bones (usually steel rods) capped with thicker ends (the ball-and-socket joints proper). This contrasts with wire armatures, which are more or less uniform in thickness, and flexible throughout.
left: wire armature covered in masking tape, and reinforced with plumber's epoxy; right: ball-and-socket armature
The flexibility of wire armatures can be useful sometimes, but more often than not you'll want to reinforce the "bones" so that limbs can bend only where joints would normally be. While this isn't a problem with ball-and-socket armatures, the problem you might have there is adjusting the length of the bones. Off-the-shelf ball-and-socket armatures are often sold as kits which include the joints, and long steel rods which you are expected to cut down into segments of desired length. Cutting steel can be somewhat problematic if you don't have appropriate tools, so you might want to consider getting something like a Dremel multitool - it will help with this as well as other fabrication steps.