Much of this has yet to be decided by YOU. You cannot design a system and then decide what to do with it. That's kind-of backwards. You have to make the decision on what the desired/required output is and balance that with the expected load that will use it, which will in turn determine the battery required, voltage, and current.
Batteries are all roughly the same as far as their efficiency is concerned. They differ in their chemistry and capacity in Ampere hours (Ah) or milliampere hours (mAh).First you have to decide what your use will be: what voltage and what current will your application circuitry require, and for how long should it run on the battery alone?Then choose the battery, to provide the required voltage and current, for the desired hours. Then choose the charger/solar cell options.
Solar panels are really only good for directly charging batteries where the solar panel voltage is higher than the battery voltage thats being charged.Solar panels dont work well with switching converters especially in low light, as switching converters need something that approaches a voltage source when they start, and solar panels dont behave like this.What usually happens is that as the solar panel voltage rises as the light intensity rises, eventually the switching converter will try and start and will try and draw current from the panel , which cant deliver enough so the panel voltage collapses, and the switching converter then goes into an unstable state where it may sit there drawing current but not switching, ie it wont start.The simplest solution is usually the best, ie use the solar panels to directly charge a battery via a blocking diode, and then run everything else off that battery.
The general rule-of-thumb is use PV panels with a voltage of 1.5 x battery voltage.In low light conditions the output voltage drops considerably, and the open circuit output voltagespec of a panel is only for full tropical sunlight conditions.So for 5V that means 7.5V panel (or more to allow for regulation losses).The other approach is use a boost-buck converter with MPPT so that the voltages can be different,and this is what a good solar charger can give you - the MPPT is going to optimize the load thepanel sees.You could stack your panels in series groups of two, and then use a buck converter to drop down.(remember the extra diodes to prevent reverse driving of shaded panels if you stack in series).