Is there a single convention used to express the wind direction?
As far as METARs are considered, the wind direction gives the direction from which the wind is coming. From METAR definitions:
The direction, in tens of degrees, from which the wind is blowing with reference to true north.
So, Wind 270 shows that the wind is coming from west.
The reporting in ATIS and tower is the same, only difference being that the reference is magnetic north, while it is true north for METAR.
Wind numbers say where the wind is coming from. Wind 270 means that the wind is coming from the west, and blowing towards the east. If you point west (270), you will have the wind in your face as a headwind. If you point east (270 - 180 = 90), you will have a tailwind, or the wind at your back.
Another way to think about this is if you want to take off from runway 27, where you are pointing to 270, (pointing west), you want the wind coming from 270, so that you have a headwind.
It's easy to remember that when you are on runway 27 you are pointing to 270. Just remember that a headwind aligned with the runway will have the same number, and you will remember that the wind direction is where it is coming from.
I always use the old saying;
The North wind doth blow, and we shall have snow...
Since this saying originated in England and in England it is colder to the North, we can conclude that a North wind blows from the North.
Incidentally, it is precisely the opposite with ocean currents. The Gulf Stream is a North-Easterly current, because if you are floating in it, it will take you to the North-East.
As a pilot, you really want to know the wind direction on takeoff and landing. The reported direction will be where the wind is coming from, that is, opposite the direction the windsock is pointing. A good rule of thumb is that if the direction is reported in writing (METAR) then the bearing is relative to true north; if by voice (ATIS) then relative to magnetic north. This makes sense from the perspective that ATIS is related to a specific airfield, whose runway directions will be numbered according to the local magnetic variation. At an untowered field, pick the runway numbered closest to the ATIS-reported direction.