Recommendation for power supply

I had just got an idea of making a binary clock using an arduino pro mini and I wanted to power it wirelessly, but every project I do I get promblems only regarding the power supply.
I do electronics only as a hobby and I am no engineer, so can you please give an idea about a power supply to power arduino wirelessly for running it 24x7.
I have thought of using a Li-ion battery. Is it good?
Please give me suggestions on how to use it.

kamehamehakosu:
I do electronics only as a hobby and I am no engineer, so can you please give an idea about a power supply to power arduino wirelessly for running it 24x7.

Does that mean that your Arduino is using a wireless module to transmit and receive data OR do you mean that there should be a wireless connection between the Arduino and its power supply (similar to wireless charging for smart phones).

...R