Seems a bit overkill in my oppinion, but if you have the space, there is no issue using them. I always use the smallest ones with about 2500 mAh. Adding LEDs will be no issue as well (asuming we are not talking about high power LEDs, but LEDs with a current of about 20 mA).
Some further words on the maximum current issue:
I found several current limiting factors, but none of them should apply in this case, so in theory you can feed all your needed current through the micro-USB port of the nano. Lots of older entries say, that 500 mA is the maximum, but that's because USB was once specified that way. Every USB wall charger or powerbank supplys more than that.
I still am a bit uncertain to feed high currents (> 0,5A) through the nano, but in theory it should be possible.
But be careful when using the VIN pin for power supply afterwards agin! The voltage regulator connected to that pin has strict limitations and even though you may power a lot of things via USB it may fry the nano, if you try to power them via VIN.
You won't get much trouble, but a small cloud of funny smelling fumes will tell you, that the regulator quit it's job.