I am no pro at turning, but have to do it every week to produce some small parts. Usually just in brass. I used to buy just the brazed straight carbide cutters from Mcmaster Carr. They have two types of carbide. C2 and C5. They do a pretty good job there explaining what each works best on.
Even the bras I turn will eventually wear out the carbide tips so they get dull. If I let a little chatter go on, the tips are likely to chip and break. Once that starts, they either need to be thrown out or possibly sharpened, depending on how bad the chip was.
It is absolutely critical to have carbide aligned properly to the center of the work and that there be as little play as possible in the carriage and tool holder.
If you have any slop at all there or it is difficult to adjust to perfect center, then HSS will be the best choice. You have to turn slower with it, but it can easily put a very nice finish on steels.
If you are using hardened steel, then you would be better off grinding it first or heating it up where you will be turning. Hardened stuff will certainly chew up some cutters of any type.