I've used this USB battery:
https://www.ebay.com/itm/5V-1-5A-Mobi...ht_1502wt_1164

with a set of 4x18650 (TrustFire blue cells, about $7 a pair at dx.com) cells. Total cost under $30 for 8000 mAh of USB power and drives anything that can run off a USB socket.

It would be cool if that device could "reverse" itself and charge the 18650 cells from another USB power supply.

FWIW, you can buy these off of eBay for < $4 shipped, with a nice plastic case. I have a few of them. One caveat, when using rechargable batteries, these will DESTROY rechargables because they run the batteries dead flat, which is very bad for rechargables. It's exactly what you want it to do with alkalines though.

I use goal zero's smallest solar charger that can charge AA and AAA batteries and USB. Works with my iphone 4s

If your referring to post #26 by Joewin, it can....be charged by USB wall charger and deliver USB power....Just not at the same time... I have one. Most economical solution..

In addition to the common USB wall charger, I plan to charge it on bike with this:

https://www.thinkbiologic.com/products/reecharge-dynamo-kit

I have the wheel dynamo and the recharge ($25) just need to cut off the plug and wire a female usb a to the end and figure a way to keep it waterproof.

That's exactly how it works. I normally charge the 18650 pack off a USB port of a PC over night.

I also have a USB adapter for my dynamo hub that could be used to recharge the battery back for longer trips away from the grid, but so far I haven't had any rides long enough to require that.

One other nice thing about it is that I could make it lighter by removing up to three of the 4 cells and downgrade its capacity for shorter trips, if I was concerned about weight.

When it comes to batteries and chargers I make use of Motorola. They're reliable especially for long trips.