Anyone know what the minimum supply I can use is?

 

It depends on the processor present and all the connected hardware. Check data sheets for the current figure - always plan on having a healthy reserve of about 50%.

 

I was thinking more voltage wise. It has an ATMega328-PU. I'm not too worried about current at this point.

 

Try looking at the datasheet for the board. The micro can go down to 1.8V but the rest of the board probably either needs 3.3V or 5V plus if it has a regulator then you should add about 2 to 3 volts on top of it.

 

The ATmega328P will operate from 1.8V to 5.5V in. At voltages
below 4.5V you need to reduce the operating frequency below
the maximum frequency of 20MHz.Check the safe operating area
graph in the datasheet.

(* jcl *)