What is the best way to render a series of images with different cameras and views of the scene, with objects in different places?
Do I need to essentially create an animation and build all of that in, or is there a different way to do it?
Yes, create an animation to easily render each image that you want. An animation is simply a series of still images that when displayed briefly in succession provide an illusion of movement. As you only want a series of still images you don't need to do any fancy smooth transitions, just position how you want things for each image.
Start at frame 1, position your objects and camera as you want, then A to select all objects and I->LocRotscale to keyframe everything. Go to frame 2 and position things the way you want the second image and insert keyframes again. Repeat as many times as you need, then adjust the end frame to match how many frames you have setup and have the output file type as still images. When you use the Render Animation button blender will render each image for you.
While you can use timeline markers to switch cameras during an animation, I expect you won't need that, just position and keyframe the camera the same as every other object.