Not knowing what your residence looks like, supporting structures, the terrain around you house, its hard to tell. If you have a chimney, a bracket can use that , that you can get an external antenna up. Low band would work, with your terrain not hampering you too much. Vhf, terrain starts to kill you, uhf and 800 mhz, are tough. Even a 100 ft tower, if you got hills around you, you got troubles. With increased height, you could get increased interference. A minor structure, will give you the county you live in, and you should get the state frequencies. Cost, say, $200-$250, that includes the outside antenna, coax, the structure to put it on. Maybe that figure is high, you could use rg-8x coax instead of rg-8 sized coax, a smaller bracket or pole top mount an antenna on, and there are many different scanner antennas that are cheaper. An outside antenna will make signals clearer, so you don't have to get too exotic.
DPD Productions - Base & Mobile Antennas for Radio Scanners: VHF, UHF, NOAA, Low-Band, 700 MHz, Police, Fire, Public Safety
This site has many different scanner antennas ,