The capabilities of the Leonardo are slightly better (p.e. 2.5kB RAM instead of 2kB), so you probably won't regret replacing the UNO with a Leonardo. Keep in mind that the Leonardo uses a different processor, some pins are multiplexed differently and many shields are only compatible with the UNO without tweaks. All the official Arduino shields are compatible with all Arduinos so you won't get problems with the Ethernet shield or the WiFi shield for example. The vast majority of shields work with the UNO, some of them may have problems with the Leonardo. The SPI and I2C interfaces are on different pins for example.
For the Leonardo you'll find examples in the IDE how to activate the mouse or keyboard functionality, this should be pretty easy. For your project the Leonardo is clearly the better choice.