If your doing a a through you will be fine with a starter or intermediate tap and running it through. If you want to tap a blind hole then also get a plug tap, so you form a full thread to the bottom of your hole.
If your tapping metal by hand then normally go about 2 turns in, then half a turn out to relieve the swarf. Also use a bit of lubricant on the tap to help. If you only doing occasional work don't bother buying tapping goo just use a few drops of oil.
Using a machine tap in the end of a drill is a real rough arse way of tapping holes and with something as small as M3 you won't have any success.
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