Arduino - Easy to learn microcontroller. In my opinion Arduino is probably the easiest to get up and running when interfacing to other electronics, like LEDs, switches, sensors, and actuators. The one weakness would be communication to the outside world, as there is no native Ethernet or WIFI interfaces. They are available to buy these as add-ons. Arduino are also good for real-time projects, as they have no operating system, so no spurious interrupts to mess with your designs timing.
Raspberry PI - More like your laptop computer than a microcontroller. If you want a graphic GUI, or some real computing horsepower, then PI is the way to go. You can use the PI general purpose input output (GPIO) pins to interface with other electronics. I would say its medium difficultly to do so. The nice thing is that PI's come with Ethernet or WIFI, so its easy to use remote communication with your project. PI's are not good for real-time control projects, as the operating system has many interrupts which will cause delays when trying to execute real time code. Another advantage of using a PI is you can choose between many different languages. So if you are not a C language wizard, you could use Python instead, which is easier to learn than C. Raspberry PI I2C interface timing Raspberry PI SPI bus interface timing
LPC845-BRK - This is a ARM Cortex M0+ microcontroller. I would put this in-between the Arduino and the PI. The LPC845 offers a fast 32 bit processor running at 30 MHz with a bunch of programmable GPIO. Like the Arduino, the LPC845 is running C code on bare-metal, so its good for doing real-time applications. If you have C programming skills, it will make learning this board much easier. LPC845 information