I can usually remove bolts and not damage threads, I can always helicoil it if need be.
Drilling a hole, if I can't do it on the milling machine, is a lot easier with a small air drill. You start with a very small drill and you can correct the location with a centre punch, you just chip the side of the hole away to move the drill over. The larger the hole gets the less you can correct it's position.
If you going to buy stud extractors[easy outs] the best ones are fluted rather than the spiral left hand thread. The spiral ones work some times but I often find they split the bolt and make it harder to get out, the fluted ones you hammer into the bolt, after drilling a hole, they work more often than the others for me.
If it's likely to be loose sharpen a drill to cut backwards[I know it won't cut very well] then try drilling it out, sometimes fasteners unscrew.
Another very good method is chemical, steel bolts in ali can be burned out in sulphuric acid[battery acid] it leaves the threads lovely and clean[anodised]
I have a gearbox case here that has a snapped stud and someone has drilled off centre. I am going to try soaking it in Alum, it's available in Tecos, can't remember what it's for. I am told a warm solution of Alum dissolves steel, but doesn't do anything to ali?