Lino block prints are fantastic home made rubber stamps. I love making linoleum block prints of dolphins and fish. (But also out of any other cute animal or sea creature.) Simple cute cartoon sketches or line drawings are perfect for linoleum block carvings. It's fun because it gets you thinking shapes rather than contour outlines. You also have to think in reverse patterns and mirror images. They turn on my creativity because I can get into hands-on carving and shaping which stimulates my thinking in 3D.
For making linoleum block prints you draw your design onto the block REVERSED. You can use carbon paper to trace your design right on the block. Make sure if there is any writing or logo that it is backwards. Then you carve out slivers bit by bit from your block WHERE YOU WANT white (or the color of the paper you are using), or blank space, or no ink, or absense of paint.
Linoleum is a very hard substance so carving blocks of a softer rubbery material are also available (see below). I like both. Each gives a different feel. You have to try and see what feels best to you. Both are inexpensive and easy to use. My hand slipped a few times with the harder linoleum block carving, so I switched to the master carve rubber blocks (also called softoleum). There is less slipping, but the cuts are different and print pressure is different when you go to block print. You will get a feel for it as you practice.