Power converters are boring, but important. The lipo battery needs to be safely charged, and then its output regulated to 3.3V. The regulator needs to have acceptable ripple, but also good transient response (sudden jumps in output).

To make the prototype easy, I'm starting with an Adafruit PowerBoost 1000 Charger.  It won't be economical and size efficient to stick with that in the final version, though, so I'm designing a power board based on the same chips (TPS61091 regulator, MCP73871 charge controller):

https://github.com/frezik/lipo-power-board

This is split out of the main design so it can be tested as a prototype of its own.

On another subject, received the PCBs for the prototype button matrix. It came faster than the batteries and LCD screen, oddly enough.