Starting With An Arduino Uno
If you need inspiration what to do with the Arduino, google Simple Arduino projects and search a bit. You will find a lot of interesting things.

If you want to build a keylogger for a normal computer keyboard, then you can start with an old PS2 keyboard and this library: PS2Keyboard Library

From a quick glance on the PS2 protocol, it seem to have the same electrical functionality as the I2C protocol (both lines have a pullup resistor to 5V and the connected controllers are open collector, so that an inactive device doesn't disturb communication on the bus). With this I would say, you have to tap the Data and Clock lines with the library. Maybe you can also power the arduino directly over the bus power lines.

Maybe this video is also interesting in this context: Hardware Keylogger with Arduino UNO

As the USB protocol is far more complex than PS2, I wouldn't recommend a USB keylogger as a starter project. (Though it seems possible when using the right shield for the UNO). You can also use an USB to PS2 Adapter for your USB keyboard to get it working without buying a new keyboard. If you still want to make a USB keylogger, I think other Arduino variants can also work as USB hosts, which would make things easier.