Well, as I'm sure you've read, discone type antennas are a popular option.
They have a wide useable bandwidth. Most hobby grade antennas are in the range you are looking for, although the discone design is not limited to just that.
The drawback is that they have zero gain. While not an issue if you have a strong enough signal to work with, and are using properly sized coaxial cable (based off length of the cable run), it can be a drawback if you are out on the fringes of the system coverage.
Getting an antenna with some gain isn't impossible. Since the ranges you probably want to listen to are in the public safety portions of the band, you can easily find tri-band antennas for the amateur radio market that will provide some good gain. Dual band is an option, also, although it'll probably have some issues up in the 700-800-900MHz area.
What really makes a big difference is to get the antenna outside your home and up as high as you can safely get it.
Since VHF, UHF and higher tends to be mostly line of sight communications, the higher up the antenna is, the father off the radio horizon is. In other words, the higher up, the more it can see.
The other portion of this is that you must have suitable coaxial cable to get the signal down to your radio. Since all coaxial cable has some amount of loss inherent to it, you will lose some of your signal in the cable.
The amount of loss will vary by frequency. On lower frequencies, the amount of loss in a given cable will be less than at higher frequencies. As your frequency goes up, so will your losses.
Also, as cable length goes up, so does the loss.
It's important to install suitable cable for what you are trying to do. Putting the time and effort into installing a proper antenna and then connecting it to your radio with cheap cable is going to lead to some disappointment.
It's usually a good idea to figure spending at least as much on your coaxial cable as you will on your antenna.
Depending on the length you need, something as simple as cable TV RG-6 might be sufficient. If the run is longer, you'll need to upgrade your cable. Often hobbyists will use LMR-400 for many uses. It's a cable that sort of mid-range for hobby use. It's thin enough that it's easily routed through your home, but it's big enough that for reasonable distances, it works well.
If you have a really long cable run, LMR-400 may not be sufficient and you may need a higher grade cable.
Either way, go into this knowing it's not going to be cheap. Take your time, plan out your system well, and get good quality stuff.
Also, do not overlook the importance of proper grounding. Putting an antenna up in the air and giving it a nice cable down to your radio can be asking for lightning related issues. Make sure you understand the grounding requirements shown in the National Electric Code. Don't cut corners, don't ignore it, and always ask for help if you need it.
