Firstly, unless your drill is sharpened properly it will always drill oversize because the centre is rarely if ever central!
Secondly, at that size if you run the drill in and out a few times after breaking through you will usually enlarge the hole and make it oversize.
Thirdly, if you start threading with the correct tap, ( a taper tap ), you will automatically open the hole to the correct size for the thread. Always finish off with a second tap or plug tap.
Fourthly, always use cutting compound on the tap. If you haven't got the correct stuff then use a medium oil such as engine oil and keep applying as you tap.
Fifthly, once the thread has started to cut, it's 270 deg clockwise to cut and 180 deg anticlockwise to break the swarf.
Learnt all that as an apprentice nearly 50 years ago and I've never broken a tap yet!
Hovrin