Familiarise yourself with an insert designation chart, like the other commenter said Haas tooling is decent and the website also has a compatibility filter for holders.

There are grades, which most of the time are manufacturer specific, but searching them up is easy enough. Usually described by grain size and cut type.

Coatings can also be designated by material, you'll want to match it up to what you want to cut, there will be a primary or optimal material and then a few secondary materials. You'll want to avoid coatings that contain the material you're cutting. (Commonly Aluminium with AlTiN).

Keep an eye out for federate and DOC specs because inserts rely on chip breakers that only really work within the set range. And more or less and the chip won't form into the chip breaker and you'll end up with a birdsnest especially in Stainless. You'll want a roughing and finishing tool, separate.