With 304 and 316, technique is just as important as the tap quality. Both materials will work harden quickly if the tap is "pecked" (start, reverse, start again, etc.) which is the most typical reason for tap breakage. So I only machine tap those materials which is why I set up my mill with momentary forward/reverse buttons specifically for tapping. as well as auto-reversing. And I plunge to full depth before reversing. Lube is your friend here. And I spot SS with 140° spotting drill and pilot drill exclusively with cobalt 135° points.
At M6 and larger, the risk of breaking a tap in 304 or 316 is much less than on smaller sizes. So at M6 and above, I generally use high grade HSS Morse taps that are either steam oxide or TiN coated - these are available from
Maritool. Anything smaller than M6 I use cobalt steam oxidized taps available through
McMaster.
M4 and M3 deep bottom tapping in 304 is the most challenging since the tap needs to be spiral flute to extract the chips, and I typically pilot drill 0.1mm oversize in those situations if possible. On M4 or smaller, if at all possible, I will drill through the material and use spiral point tap even it it takes longer and requires longer drilling time, just so I can avoid using the more fragile spiral flute taps.
I'm sure there are other formulas and tap brands that work for others, but this is what I have come to after lots of broken taps and burnt-up drills.