The ATmega328 processor runs at 8MHz with the internal oscillator, a better choice (than the 16MHz of Arduino 2009) for the LiPo voltage of approx 3.7V. The display I used is compatible with the monochrome 128x64 OLED display from Adafruit.
It is powered at 3V3, requiring a voltage regulator (78L33, TO-92), placed where the the trim-pot (for adjusting LCD contract) was supposed to be (top-right corner of the board).
The sketch uses Adafruit_SSD1306 library, with the wiring to the display as defined below:
#define OLED_DC 8
#define OLED_CS 7
#define OLED_CLK 4
#define OLED_MOSI 3
#define OLED_RESET 5
Note that the same D3-D8 are used for connecting to the LCD 1602 display in the "regular" DIYGeigerKit.
Also note that I did not install the "click" LED nor the buzzer, relying instead on the OLED display to indicate the radiation level.
If I were to improve on it, I would replace the right-angle toggle switch with a straight-up one (easier to operate), then add a button or two for user inputs (configuration parameters, menu navigation etc). The "click" buzzer and the LED could be made "digital", wired to controller's outputs. Adding a Bluetooth module would be also useful (if it works at all from inside the closed box, I need to try it). Ideally, I would also add RTC, GPS and SD card, for logging purposes. And then it would become a smaller and cheaper version of Safecast bGeigieNano :)