I try to sense a VLF magnetic field (1-100Hz) by using a coil. The field is very weak and in most of reading there is too much noise. Is there the most important characteristic of the coil, should I look at first if I want to improve my readings?
Generally speaking, the "loop area" (the area inside the coils of wire) is the primary factor that determines the sensitivity of a loop antenna.
If the noise is also magnetic in nature, there isn't much you can do other than try different orientations of the coil to maximize the signal-to-noise ratio. Increasing the loop area in this case will only increase the noise, too.
However, a large coil can also couple noise from electric fields to the circuitry it's driving, and it may therefore be helpful to wrap your coil in a grounded electrostatic shield. I've seen loop antennas created by pushing multiconductor cable into a piece of copper tubing, bending the tubing into a circle, and then connecting all of the conductors in series to create a coil. But be careful to leave a gap in any such shield; otherwise, it will create a "shorted turn" and eliminate any possibility of detecting magnetic fields.