scanners do not interfere, be cause THEY ARE NOT transmitters
While we're picking nits, that's not necessarily true.
*gasp!* What?!
Anything that runs on electricity transmits RF interference (RFI). If one appliance is generating RF on a particular frequency that another finds itself susceptible to, then it will be noticeable. Generally speaking, though, scanners and other electronics are shielded to prevent/minimize RFI. That's why we use coaxial cable with most of our antennas.
Can a scanner interfere with another radio? Sure, but generally only from an RFI standpoint. Consumer-grade scanner-only radios aren't built with transmitters necessary to make useful transmissions.
Today's consumer-grade ham radios usually can scan other channels and can transmit usefully (in that sense, they ARE scanners that transmit), but the scanner part is usually limited in their function as compared to late-model scanner radios. I'm not aware of any consumer-grade ham radios available to consumer that can track trunked systems. A ham radio can be used (with proper license) to transmit on ham-radio frequencies. It cannot be used legally to transmit on commercial frequencies, even with a commercial license. I'm a big fan of the Yaesu FT-60R.
A commercial-grade radio may also have a scanner in it, but they are usually even more function-limited than ham radios. And they're usually limited to a single band and are not field programmable. OTOH, commercial radios usually have a higher build quality than ham radios and scanners. Their receivers generally perform MUCH better. That, and they can be used to transmit in commercial AND ham bands. In other words, they do less stuff than ham radios and scanners, but they do what they do VERY well. And you can usually program them to not transmit on a per-channel basis. Motorola and Vertex are my favorite manufacturers here.
The bad news: for $50-100 you prolly won't find anything high-performance and recent in the ham and commercial realms. So, if you're not willing to sacrifice features and performance, you're gonna be wishing you had 2 or more radios.
A side note: There are single radios that can "do it all"---Wulfsberg's FlexComm products come to mind. But they are so expensive that there's really no point. Many of these systems are made of individual radios that are tied together, so it's not as elegant as a single-box solution. And, I don't think there's anything like this in a handheld. Yet.
HTH