For stamps that I use at reenactments, I prefer to find old German wooden stamp handles, strip off the old rubber and re-use the handle. I search for “Holzstempel alt” or “Holzstempel Konvolut” on eBay. de. I look for old rubber stamps and stamp handles at antique shops and flea markets, too.
Wood stamp handles in a period-correct style are still made and available in Europe. Jackson Marking Products is a US source for handles in the proper style. The 1-1/2″ round stamps are a perfect match for the most common sizes of the round Dienststempel stamps. There are also various kinds of modern stamp handles from various sources that can be used, including wood ones that can pass for something from the 40s.
For stamps that I only use at home, I cut simple wooden blocks. I used to use a cheap back saw and plastic miter box from the hardware store. Now I use a band saw. I just cut up pieces of scrap wood. You can buy small, smooth pieces of wood at a craft store, that are easy to cut to size.