it sounds like you want to have a power supply.
battery
charger
voltage regulator
if you get a cell phone battery pack, the battery inside is 3.7vols.
you can connect a booster to pump that up to 5v, tied directly to the battery.
as for speed of charging, I get paid on Fridays and by Wednesday, I am low, the money goes really fast.
so, by fast, if you mean about 4 days, you should be fine with any charger.