I use DS1820 one wire sensors. I've tried a multitude of different temp sensors, including thermocouples, and the DS1820 series have provided the most consistent, accurate, and reasonably simple temperature sensing for an Arduino based controller.
Small tactile switches are easy to interface. There are plenty of tutorials at the Arduino playground
I recommend starting with a serial LCD before trying to tackle the Nokia display. They are cheap and somewhat easy to use. If you have limited programming knowledge, I fear that you'll be frustrated with the Nokia.
Use a simple control algorithm. You don't need PID or anything fancy. Use a variable (integer or float) to hold your temperature setpoint. Give yourself a temperature differential of 1 to 3 degrees. When the keezer's temperature is greater than setpoint + differential, turn on the relay. When the temperature is less than or equal to the setpoint, turn off the relay.
Include a short cycle timer to prevent the relay from triggering quickly and wearing out the compressor. Set a 5 or 10 minute delay so that the relay cannot be triggered again within the delay period (after the relay is turned off). Use the millis() function to measure time elapsed.
Your control code shouldn't be more than about 30 lines. If you use a DS1820, you'll need to include the OneWire library