I made a really Tiny Altimeter from here that is working good. It consist of an arduino pro mini, ,the display ,a sensor bmp085 a battery lithium 3.7v 1000mAh and the charger for the battery tp4056 board. I try to connect display through hardware spi but i have display shifting , so i connect it with iic.You can allso find files for a 3d printed case and code for Tiny Altimeter at the upper link.
Next photo is arduino pro mini with the display (0.96 Inch 6Pin IIC I2C OLED White LCD Display)
Like a SandSwitch , i place the baterry upper ,but as proved 1000mAh is really big capacity. It doesn’t need so much , a 150-300mAh is good enough
I made all wirings and placed board on battery