It appears to have two environments on one board, and I imagine the Arduino environment works the same as any other Arduino. All I know about the Yun is that it comes equipped with USB, SD, Ethernet, and WiFi, yet appears to have the same memory arrangement as a Uno. That looks like the kiss of death to me, but you need someone more qualified to comment, and you may find it OK for your purposes.
Yes, it is two environments in one: a Leonardo, and a 32-bit Linux computer. The SD card, Ethernet, WiF, and USB host interfaces are all managed by the Linux side, so the memory limitations of the Arduino side don't come into play. You can handle much of the network communications, file I/O, etc on the Linux side, and reserve the Arduino side to handle just the timing critical real-time control and hardware interfacing. With most of the peripherals handled by Linux, you have much more power: a full web server implementation, WiF configuration and management, file system management, and lots more, all without consuming ANY of the precious Arduino resources.
I've done quite a bit with the Yun, and I've only scratched the surface. Picture a Leonardo connected with a serial port to a RaspberryPi, but replace the video output with on-board WiFi. It's kind of like that.
So, in conclusion, should I or should I not invest in a Yun having the criteria mentioned above (size, budget and capability to serve my purpose)?
I would go for the Yun: smaller than a combined Uno and a WiFi shield, and lots more powerful.