You can get the starter materials real quick! Google “speedball Lino set” and get the handle which should come with a number of blades. You should be able to find this for $10 or under.
Most of the time I carve on the speedy-cut pink rubber blocks that you will probably find listed right by the link cutter. They are easy to carve, relatively cheap and fun. I have tried carving using real linoleum at this point and I ripped a 3/4 inch blister open on my middle finger doing so. Linoleum is pretty hard and the speed ball cutters aren’t really designed for it.
I really enjoy stamp carving and enthusiastically encourage you to check it out!