Pretty much all 6-9 speed Shimano derailleurs should be compatible. The pull ratio of all of them is the same.
The main concern is that the derailleur "capacity" is enough to take in the slack from the chain when you're in the small-small combination. Looking at your cassette, that's unlikely to be an issue; it doesn't look like it has a very wide range (looks like maybe 11-25?).
Shimano does document the capacity of their derailleurs, so just look up and check before you buy. The capacity needs to be at least the difference in cogs between the smallest and largest sprocket in the cassette plus the difference in cogs between smallest and largest chainring. Some derailleurs have (in addition) limits on the smallest or largest sprocket they can handle. But honestly, I doubt you'll be able to find one which won't work.
Would a shimano tourney or Altus be the right thing?
Either of those, or Claris or Sora, would likely be fine.
An example derailleur that would probably work is the Claris RD-2000-SS:
According to the official specs (as listed on that page) It requires at least 25 teeth on your lowest (largest) sprocket, a maximum of 16 teeth difference between your smallest and largest chainring, and has a total capacity of 37. From my limited experience and from reports from others, you can usually go a bit outside the stated specs without any problems, but unless you're running a triple chainring or have a particularly wide-range double I'm guessing that this one would be just fine.