Struggling to get my first lens upgrade

What's your camera? On an Olympus body, i think the 45-200 beats the 45-175 because of IBIS issues, on a Panasonic, the shorter tele is probably the better choice.

As for the 9-18 vs the 20: the focal lengths may almost overlap, but they really are very different lenses. At the long end the 9-18 is more than 3 stops slower, so if you can take a particular photo at 1/500 s with the 20, the 9-18 needs 1/40 s or so. That's a big difference, so if you shoot portraits or semi-wide scenes at difficult light conditions, the 20 is vastly better. The 9-18 on the other hand is a very nice wideangle zoom, so if you do a lot of panorama or scenic shots, you should consider it.