Here's a publication that may help determining the profiles for different materials. I've been using HSS for 90+% of my turning and facing needs since the 1980's. If you grind them right and pay attention to feed and speed rates, they will give mirror finishes on almost any material.
Here's the section on HSS metal lathe tools
sharpeninghandbook.info
With a lathe turning at only 340 rpm carbide will do much more rubbing than cutting. I use HSS exclusively on my Seneca Falls lathe. It has a maximum of 670 rpm.
Keep in mind the minimum nose radius of the tool should be 1-1/2 times the distance it moves with each revolution of the spindle. This publication recommends 4 times the distance moved for glass smooth finishes.