There are actually many, many variations of "headset" mics, and obviously they come with many, many different prices tags.
One of the most popular is the Countryman E6, which has a very small profile visually, so it is favored by performers, clergymen and other public speakers, and it is an excellent mic. I personally use a Sanken COS-11 microphone with a Sennheiser SK100 transmitter. I use these primarily for stage use in Musical Theatre and in my vocal quartet. The mic is very small and is usually "glued" to my face in front of my ear, or sometimes in the hairline, if the style permits.
One thing I like about this style of miking is that the sound has a much better "ambient" quality to it, rather than sounding like the close miced sound of a DJ for instance.
I have used this same mic for puppetry and the way I do it is to run the wire straight up the back of my head and over to the forehead. Then I use an ordinary gym headband to hold it in place directed down towards my mouth. It works really well.
The best advantage to wearing a head mic is that it always remains a constant distance from your mouth, regardless of how you must contort yourself in order to puppeteer. This way your sound engineer (if you are fortunate enough to have one) does not need to be constantly adjusting your gain. With a "lav" mic you can easily turn your head/mouth away from the mic, or equally bad, turn your head straight down and bark straight into it. They are also much more prone to rubbing against clothing, props, arm rods, etc. etc.