Charging a LiPo is quite a complex procedure that requires some additional hardware and a controlling micro (which you have got). Energy losses are comparably high, so this method will be recommended, when the amount of harvested energy is high, Charging a gold cap (protection circuits!!!!) could be a good alternative with a minimum of effort. Try first with the recommended 220µF cap to see what happens.
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You need to calculate your energy budget. How much energy to you need to the measurement, how much for the BLE transfer, and how much energy can you generate by the harvesting?
Small LiPo cells (in the 100mAh range) can be charged by quite low currents (down to 1mA even). The LTC4071 can do this quite efficiently (its a shunt regulator, so its not wasting energy during charge). Or you configure your energy harvesting so it doesn't output more than 4.1V, then you don't need a regulator (did this before, works quite well). LiPo batteries are not as efficient as capacitors, but they store much more energy.