Battery of Arduino ONE

Hi! I just created a programe for my arduino ONE but I want this programe to be able to run by itself without the need of being always connected to the computer or to anything at all. Like a battery, I just do not know what batteries are compatible with this arduino. My idea is to have my arduino always connected to a small rechargeable battery and obviously, after some time this battery will run out, that is the moment to charge the battery.
I don't know if this is possible, please help me