The most important rule in buying any puppet is to make sure it complies with toy safety regulation (this rule applies to any toy bought on e-bay). Check with the seller that it carries the EC toy safety logo on the puppets tag (second hand puppets should still have their fabric tag with the logo on).
Beware of very cheap puppets made abroad, contact the seller and make sure that they comply with the toy safety regulation, if not DONT BUY.
Definition of Puppets -
FINGER PUPPET - a small puppet designed to sit on the finger, doesn't have moving arms or mouth.
GLOVE/HAND PUPPET - a larger puppet that just covers the hand (like a glove) usually with moving arms and head (some may have a moving mouth).
LONG SLEEVE GLOVE/HAND PUPPET - a larger puppet that covers the hand and lower arm, usually with moving arms and head (some may have a moving mouth).
GIANT ANIMAL HEAD PUPPET - Large animal head puppet that covers the hand & part of the lower arm, with moving mouth.
BODY PUPPET - a puppet that is formed as an entire animal or person, these are usually large in size.
Don't be afraid to ask questions, a reputable seller will be happy to tell you everything you want to know about a puppet. If buying second hand always be sure to get exact details of the age & condition of the puppet.
I hope this little guide has been of help, if you need any further advice or have any questions please contact me.