If a small non robust lathe or a limited use grind yourself from decent quality an HSS 5-8% cobalt tool steel up with the full profile.
More rigid machines the indexable ones work very well as long as the tool is robust. ie the cheaper ones from asia dont bother even at over £62, they flex and total waste of money i have a few plus one from an advertiser on here German sounding which is like butter another £30 odd wasted.
Go without and save up for one good one from decent brands as Kennametal, Ceratizit, Seco, Sandvic, and the like.
If centre heights right, rigid and still sharp you can take as little off as you can. Cant do that with flexable tooling, it deflects without cutting.