Upgrading From a 9 Speed Sora Derailleur? I bought a bike on Ebay which has a Sora groupset. The rear derailleur is noisy and jumps in and out of gears despite much tweaking. I've given up on it.

What derailleur can I buy that will work as a drop-in replace of the Sora derailleur without my having to also change the cassette or shifters?

The Sora is either medium or long cage - not sure which. It has approx 3.25 inches between jockey wheel centers.

Cassette has 32 teeth on largest ring.

EDIT: Just found someone else with the same problem. Mine sounds much the same as this: Noisy rear derailleur (Shimano RD-5800)

EDIT2: Motivated by your comments and after a bit of a clean and a bit more of a systematic re-indexing as per the video linked in the accepted answer (which I just changed below) the derailleur noise is in fact much improved. It's still not perfect but it's good enough.

TY!
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.