Part of the problem is that in PP, your project file determines the framing. If you choose to start a project in 16:9, the whole project has to be 16:9. This means that any 4:3 footage is going to get pillarboxed (the black bars on the side). Without resizing your 4:3 footage (and resizing it WILL distort is somewhat), you're stuck with two options: either leave the 4:3 footage alone and live with the pillarbox effect, or you start a new project in 4:3 mode, and all of your 16:9 stuff will be letterboxed (the black at the top & bottom).
On TV, the standard when there are two formats is usually to create the program in 4:3, and letterbox the 16:9 stuff, but I've seen other producers who used pillarboxing, assuming that their viewers are using widescreen televisions.
I hope that helps.