I need to drill a threaded, countersunk hole in a piece of material. After drilling, should I use the tap, or the countersink bit first? Does it make a difference? Does it depend on the material?
Use an awl and punch it to center mark your location (so the drill bit doesn't walk).
Drill a small pilot hole (to insure correct placement of the hole).
Enlarge the hole to the tap's specification.
Countersink (without the hole as a guide you run the risk of the countersink going off center).
Tap (run it through again if you had to readjust the countersink depth).
I never seem to get the depth of the countersink right on the first try, but you can just clean the threads back up with the tap if you have to hit it again with the countersink.
This procedure doesn't really change for different materials, mostly just the level of difficulty and the quirks involved working with them. I.e., aluminium likes to gall; hardened steel doesn't like to be drilled; wood is not normally going to tap, etc. Titanium? good luck with that.