Here’s a good idea to start experimenting with Arduino, without investing into a plethora of shields: 1Sheeld. As the name somehow states, it’s one shield that can replace a lot (I counted 38 on their site). You will need a smartphone, though, because 1Sheeld connects with it via Bluetooth and simulates the shields using an app.
Once again I crowdfunded a hardware project, this time Joypad made by Microduino. Joypad is a board where a Microduino core is plugged in. It’s quite compatible with Arduino, so experimenting with it is easy.
While communication with Microduino could be better, their service is very good. My first joypad had the wrong Microduino on it (Core instead of Core+) and was soldered badly. I got a replacement fast and for free. 10 of 10 points for that!