Upgrading From a 9 Speed Sora Derailleur?
As a sort of addendum to Nathan Knutson's answer, focusing on things to do before replacing the derailleur.


Make sure wheel is fully in the dropouts and parallel to the frame. 
Properly and clean the drivetrain with a degreaser and apply a bike chain specific lubricant, not penetrating oil such as WD-40, GT85 etc. There are many videos that show how to do this. 
Check hanger alignment. From the photo it looks pretty good (cage should be parallel to the chainrings). It might be worth getting a bike store to check it with a hanger realignment tool.
Replace cables and housings. Stretchy cables and sticky housings can cause the derailleur to not index properly.
Run through a systematic derailleur adjustment process. 
Check chain and cassette wear.