Countersinks much like drills seem to be a bit of morass. Most of the cheaper multi fluted solid metal types sold (e.g. middle type) are designed for metalwork, are typically blunt/incapable of doing a neat job as supplied in cheaper form, are made of something masquerading as HSS (high speed steel) that isn't that wears in no time, and leave a mess. Especially when used with a hand drill where they often chatter and leave a hexagon shaped cone.
Countersinks anyway need to be very accurately aligned vertical to centre accurately on a pre-drilled hole.
I've had very good luck with the carbide tipped adjustable Vario
90 304555 set with HSS G drills (the best brad point i've ever seen - really worth the investment) by Famag listed at the bottom of this page. Not cheap, but great value:
https://www.fine-tools.com/bohr5.html There's a variety to do flat bottom/cylindrical countersinks too, and also a combo set. The ones I have look identical, but were branded Colt when bought a few years ago. There's got to be sources in the US…..
They cut clean as a whistle (even in cheap ply), the drill can be replaced with a rod to guarantee centering and alignment on a pre-drilled hole when using a hand drill, very long life between sharpenings and easily re-sharpened with a e.g. a Trend fine diamond credit card slip.
Granlund make excellent sinks for metal working, I've had the smaller three flute HSS variety and found they work and last well on wood. A little care is needed if hand drilling, as they will self feed if they really get going:
http://www.granlund.com/main.php?menuId=722 Toolroom quality HSS countersinks in general are often not bad for wood if well made.
The round hole ones work smoothly when well made, but can be hard to get cutting.
Lee valley do a large solid cone steel one with a single cutter that works well - it's very stable. Needs a fair amount of sharpening though...
There's probably lots more that work well. I've never had any luck with the box store varieties though, even when the look the same they generally are made of bubble gum and are not properly sharpened. Never found a hand operated one that cut properly either, but maybe there's high quality well made ones that do.....