if you want to go super cheap all you need is a really, really big nail. That's what I used to make my first branding irons to put my armadillo logo onto my leather products and used it for years. You can make a simple wood handle for it and just heat it up on a gas stove. Simple and cheap. You can also use it as a stamp for veg tanned leather.
But it I was tired of heating it up like that so I customized a store bought Walnut Hollow wood burning tool called the versa-tool. You can buy this product at Michael's craft store or online for $29.99. It comes with a bunch of useless points that you probably won't use but some are useful. The newest model has variable temperature adjustment which they didn't make when I bought mine. You definitely want the one made for wood burning because the cheaper models don't get hot enough. This project modifies the transfer point which is a round disk shaped tip. You can also use the tapered point that comes with the brand for pyrography. Check out my video for that here.
Step 1: Tools
Step 2: Secure in vise
Step 3: Draw on design
Using the hack saw or Dremel cut out the rough shape without touching your design.
Step 4: Rough cutting
Step 5: Detail
To make the eye I used a metal punch to make a tiny divit and then drilled it with a diamond bit for the dremel.