"Scanner" and "Short Wave Radio" are two seperate hobbies. While there are some (expensive) radios that can cover both VHF/UHF (Scanning) above 30 MHz, and 'Shortwave', from .1 MHz to 30 MHz, the radios used are normally very different, because the needs for each use are significantly different.
You can't 'scan' Shortwave, because it's noisy, and you'd just end up sitting on each frequency forever listening to static crashes between talk. Shortwave and Scanning take very different antennas, too. Even the closest you're talking about to 'scanning', CB, needs a very much larger antenna to receive well, and the CB channels are likely to be too 'noisy' to scan, as well. They certainly are when sunspots are up, and you're receiving from all over there!
Seperate receivers for HF, and Scanning, will be cheaper and work better.
I'd forget about shortwave for now, till you read up on it and learn if there's anything there you actually want to listen to.
As you were asked above, folks can't tell you what sort of scanner you need till you give them the city you're in, so they can look it up and see what systems are being used there.
You may only need a basic, simple scanner. Or you may need a 'trunking' scanner. Or (more and more likely as citys go to new equipment), you may need a 'digital trunking' scanner. If the latter, you're looking at about $500 from Radio Shack, either handheld or base/mobile version. The Ohio State Police system, for instance, is a digital trunking system.