There are some terrific craft stamps at your local craft store. But they usually start about $4 and go up quickly depending on their size.
You can make your own stamps from a variety of materials.
The “handle” is usually a block of wood. If you don’t have wood scraps, ask your local lumber yard or hardware store to donate their scraps . . . or use the lid of a jar. Be sure the lid is flat and not recessed (dips in the middle). Your handle should be bigger than your shape, but not so big that the edges will mark with ink what you are stamping if the edges tip down.
The stamp portion can be any number of materials: a sponge, felt, a new shoe insole, rubber inner tubing, etc. If you use a sponge, do not glue it onto a handle. A new sponge that is still flat is the easiest to cut, but you can use an old sponge as well. Just be sure you microwave it on high for 90 seconds to sanitize it. If you use inner tubing or felt, you may need to cut several layers of your shape and glue them together to get some height.
Draw or trace the shape you want onto your stamp material. Using sharp scissors or an x-acto knife, cut the shape. Glue the shape onto the handle (wood block) and let dry. Do not use a water soluble glue like white glue. Use a permanent glue like epoxy.
Use your stamp with ink or paint, but be sure to wipe it clean after each use. Or rinse out the sponge shape after each use and let dry.
You may want to finish your stamp by tracing the stamp shape onto the top of your handle so you can see which stamp shape is underneath.
You can use your thumbprint to create animals, flowers, butterflies, or any other shape you can imagine.
Example: make a thumbprint as the body of a giraffe, then add the legs, tail, neck, and head.