Whatever tools you use, they must be mounted so that the cutting edge is on the centreline of the lathe.
make yourself a centre height gauge, it will save a lot of messing about getting the tool to the correct height.
For the materials that you listed, I would think that HSS would suffice.
Learn how to grind HSS tools, the knowledge will always be useful. If you cannot find a book showing the clearance angle to which they should be ground; PM with your E mail address, and I'll look out my Apprentice notes and send you a copy.
But, +1 for the Diamond Turning tool. Easy to sharpen, only one face to grind, and works really well for turning or facing. A centre height gauge is invaluable for setting the toolbit correctly. may seem expensive to buy initially, but easy to use, and sharpen, and they last. Much cheaper than replacing tips, and more tolerant of impacts / intermittent cuts!.
If you intend to make 22mm holes, my advice would be centre or spot drill, pilot drill and then gradually open, in sensible steps. If the lathe is a mini lathe, a 400 or 450 watt motor won't take kindly to drilling 22mm diameter from scratch. To be safe, limit the cuts to 1 mm a side. Motors or control boards tend be expensive and inconvenient to replace. They always fail at the most inconvenient times, is there ever a convenient one?.
Howard