One item that hasn't been mentioned is what do you have around you? Trees can act as huge attenuation to the frequency your trying to listen to. The higher the frequency, the more attenuation.
This is why you will find that most public safety radio repeaters are located on the highest piece of land that could be found in the area the radio system needs to cover. Then a tall tower is used to get the antenna as high as needed to make sure the coverage is provided. Just how tall the tower needs to be can be computer predicted for the coverage needed.
To put this in a receive point for a scanner, if you live in a gully, your not going to hear much. If you live on a hill, your in a good location. But again, the foliage around your antenna will play on how well you can hear.
The true test is to try an antenna at the peak end of your roof on a bracket on the roof face board and see what you can hear. If you get what you want, your done. If not, it starts to get expensive putting up a tower. Don't forget the longer the coax cable between the radio and the antenna will come into play here. The higher the frequency of interest, the higher the coax cable loss will be. Long runs of coax may require a larger, lower loss cable.
One point to consider is to remember that most newer homes have insulation with a foil backing. This acts as a partial shield to radio signals. If you have aluminum siding, this makes it even worse.
If you do mount an external antenna, don't forget to ground it for lightning protection. That's a whole different discussion.
Jim