One of the most important factors to take into account when choosing a puppet is the age of the recipient. The puppet needs to be of an appropriate size for them to handle comfortably. Another very important consideration is what use is going to be made of the puppet.
For toddlers, finger puppets are probably the most appropriate, although they will certainly love playing with a larger puppet operated by someone else. Be careful though, very young children can be a little overawed by puppets that are a lot larger than they are, so introduce them carefully.
Glove puppets, or hand puppets, are great for children aged from four years onwards, and of course for adults.
String puppets, or marionettes, are more suited to older children who will be able to manipulate the control bars more easily than younger children.
