There are a number of suppliers of carbide cutters.
I bought mine from Captain Eddie. He's not been well, and his turning has slowed down considerably, but I think he's still selling cutters through his
web site. If you go back to some of his earlier videos, he has instructions on how to make shanks and handles to go with his cutters.
There is a selection of cutters to choose from. I opted for a large (18mm) round cutter, a small (10mm) round cutter, and a radiused square cutter. The smaller the cutter, the more aggressive the tool will be. You can also buy true squares - the main advantage is that they can make sharp corners in turnings, but they tend to be 'catchy' - and also diamond-shaped detailers.
You will also need so mild steel stock to make the tool shafts, some wood for handles, and some copper pipe for ferules. Therein lies the second choice you must make - round shank versus square shank. A key point to remember about carbide cutters is that they need to be presented to the wood at a slight angle. The advantage of a round shank is that it rolls more smoothly on the tool rest as you change that angle. The advantage of a square shank is that you know that the cutter is aligned to the square face, so can tell the angle of the cutter even if you can't see the cutter because it's covered in shavings. Six of one, half dozen of the other. I put the small round cutter on a square shank because I tend to use it for hollowing where it gets covered by shavings, but frankly, I don't think it makes much difference in use. I will say that it make be a bit easier to make the required notch in a square shank.
You will need to cut a notch in the end of the shank to hold the cutter, and it may be easier to cut that notch in a square shank compared with a round shank - although I don't think it's a big difference in effort. The notch doesn't have to be deep - the dimensions of the flat should be such that the cutter will be locked in place by the edge of the flat and won't be able to rotate on its own.. In a square shank, the notch doesn't have to be any deeper than the thickness of the cutter. My grinder is 6", so it tends to do a hollow grind, so I had to do some additional shaping with a file to make the flat truly flat. Not a big deal.
I have never attempted to make a shank to hold a diamond-shaped cutter. I think that would be a challenge unless you are an experienced machinist and have the tools to make the necessary recess. But you can easily use a HSS parting tool to do anything that you can do with a carbide detailer.
Drill and tap a hole to receive the mounting screw that holds the cutter in place. Captain Eddie supplies screws with his cutters (and tells you what size they are), but you may have to shop for appropriate screws if you purchase cutters from some other vendor. Tapping the hole is tedious - it's a small hole, and small taps tend to break if you get too aggressive. On my first try, I spent more on taps than on cutters!
Final point, after shaping the shank, and test-fitting the cutter, remove the cutter and do a relief grind under the nose of the shank. You want the cutter to extend past the end of the shank, but you need to remove unnecessary metal under the leading edge of the cutter so that the shank doesn't interfere with the ability of the cutter to engage with the wood.