developing an ear/ eye for these things is a good idea. You're after a nice spiral chip. If you get alot of shuddering and small flakey chips, slow down the spindle speed and/ or increase the feed (probably both to begin with). If you can't slow down the spindle, increase the drilling pressure. If you still can't get a nice spiral chip, you're SOL on that machine. One thing I would caution about, and this is from someone with light duty machines, is step drilling in too small steps - 1/8" step at a time is the minimum I would use or you'll be busting the tips of the corners of the drill and maybe getting the drill chattering as it doesn't have enough material to "bite" into. Holesawing is an option, but I doubt you'd be able to go slowly enough if your minimum is 300rpm. Likewise with annular cutters, which are even less tolerant of flexy machines in my experience. I drilled a 1" hole 2 1/2" deep into some stainless (400 series?) over Christmas and that took a looong time on my 6x26 mill, step drilling up from 1/2" to 1", though I can't remember the steps I used. Lots of cutting oil, 60-100rpm speed, need to touch up one of the S&D drills.
I do find it funny reading the advise of those with industrial machines. Drilling a 1 5/16" hole in one go on a Warner Swasey turret lathe (4-5000lb? 10hp+?) is VERY different to drilling a 1" hole on a light home shop machine. I'd love to drill a 1 5/16" hole in steel on my Atlas 618 in one go, but it just ain't gonna happen.