i'm sure more experienced people will chime in, but You want to keep it cool with cutting fluid, and at least titanium or colbalt bits. thats a lot of stainless your going through!
You have to use a cobalt bit in that 400 series stainless.
Keep the drill bit speed down! If you told us the drill bit diameter I could give you the correct speed. 750RPM maximum !!!!
IF you go too fast the stainless becomes work hardened and then you will have a hard time drilling it. You will have to start with a new bit. But do not use the NEW bit on a work hardened hole. Use it a couple times THEN drill the work hardened hole.
See drill bits must be broken in or they can chip.
Cobalt is a thin layer of cobalt over M42 steel base.
the Titanium bits are not as hard and it is a very thin coating of Titanium.
Many people do not know WHAT those pulleys in the top of their drill press are for.
And a wood drill press has speeds that are too fast.