Here are some of the ways you can make full use of the pliability of clay. If you're going to go through the trouble of animating the stuff, you might was well have some fun with the effects you an create with it. This includes squash and stretch, replacement animation, and transformations.
Puppy Pals clip: IMToys at https://www.youtube.com/channel/UCN0w...
Please see my other tutorials on how to make an armature for a puppet, as well as other stop motion subjects.
Software: Dragonframe. iStopmotion (Mac and mobile) is a good frame-capturing app for the price. I understand iKITmovie is a good free option for Windows. Stop Motion Studio is a good mobile app. If you have a favorite stop motion app, please tell us about it in the comments.
Effects compositing in After Effects and editing in Adobe Premiere Pro. I have not had the opportunity to try out free or inexpensive alternatives for Windows.
Camera: I'm using a DSLR. But if you're not there yet, a good option is a camcorder that can run a live video signal to your computer. For best results, set the camcorder to fully manual to prevent focus and white balance flicker.
Shopping for Puppet-Making:
Clay (Van Aken, Sculpy III), armature wire: Arts/craft store like Hobby Lobby or amazon.com.
Armature kit: stopmotionstore.com
16-gauge aluminum armature wire (from an art store or Amazon, not the hardware store)
For the head, aluminum foil or wood ball (craft store)
Just about everything here can be found on Amazon if you don't have all these kinds of stores in your area. You can also get animation supplies from stopmotionstore.com.