I have been interested in the same thing. There are (at least) two different brands of photopolymer stamp-making kits you can buy online for well under $200. Do a search on “photopolymer stamp making kit” and that will bring them up – as well as other information on the process. Looks fairly simple.
You could also send your designs to a custom rubber stamp manufacturer. With laser cutting so popular now, prices have really gone down. Another online search should give you some options. Good luck!