On a 9g mixed reef, I would just get a good RODI machine (if you want, you can also just buy distilled for such a small tank) and ATO. Perhaps get a hanna alk checker since alk is the most important thing and you do have some LPS/SPS. A good Refractometer and calibration solution if you don't have one. The salinity checker, just because it is more expensive, doesn't mean it is more reliable.
Your coral will suffer if you strip too much out so I wouldn't be eager to add a skimmer, ect on 9g. It also makes noise, meh.
A controller for your heater is a life saver if your heater gets stuck 'on'. Pinpoint, apex jr, ect.
For splurging, I like MP10's on small tanks. small footprint, great flow, but totally not necessary.
I would consider flow and lighting more important than fuge/skimmer on a 9g. For lighting, I love nano-box, seem to pull the best colors out of coral with them. Cheap options grow coral too though.