Is there a way to have the mouse wheel move the viewport camera, rather than just zoom it (currently it just changes the FOV)? Unreal Editor does this and I find it a lot easier to use than Blender.
One super fast way to dolly a currently selected camera, whether it is currently being viewed though or not, is to press 'g', 'z', 'z', and then drag the mouse in the viewport. The last 'z' switches the constrained axis to the Local Z, instead of the Global Z. It likewise would suffice to switch to Normal space before doing this, in which case only one press of 'z' is needed. Same goes for Local space. In fact, it doesn't matter whether you have your transform space currently set up as Local or Normal, at least not in this case, since either with work with just 'g', 'z'. If you instead remain in Global transform space, and don't want to switch into one of the others, that's the only time when 'g', 'z', 'z' will be necessary.
Note: There is a more specialized way to move the camera along its depth axis. With the camera selected AND currently looked through, you can press Shift-~ and this will put you in "free look mode" in Blender 2.8. This is the same as the older feature from Blender 2.79 that was accessed with Shift-F. Once in this mode, you can use the WASD keys to move around the scene. However, it's very slow at putting the camera anywhere new, so I prefer the 'g', 'z', 'z' method.