LiPo battery charger and LiPo voltage to 5V booster in one package. I find mounting it such that the micro USB connector protrudes through the enclosure to be a bit dicey.
I use a conventional PowerBank. It charges mobile phones and connected to the USB port of my UNO my project is mobile. The PB is charged either by a PC or by a conventional USB-charger.
One CR2032 or two? Each cell is only 3V and won't power either the 3.3V or 5V devices. Depending on the current draw, you will lose a lot of power in the battery due to its internal resistance. Your Lipo idea was much better. The Powerboost 100C is a three-in-one device. It will accept a micro USB to charge and power the circuit, then when the USB is disconnected use the LiPo to power the circuit and in either mode run a boost converter to give 5V out. It also has some warning LEDs and signal available the Arduino can read as digital inputs. It's a pretty slick unit, except for the mounting.
Using Lipos with projects requires a good deal of care.
An automatic low voltage cutoff @ circa 3.0V is essential safety wise, let a LiPo go much lower than that and they can be dangerous to re-use. We know LiPos catching fire or exploding is not unknown.
Its not clear if the Adafruit product actually cuts off the battery when it gets too low, it only claims to have an low voltage indicator LED, which is only useful if you see it and switch off. If the batteries go flat in use, its easy to slip in Alakalines if I dont have the time to wait for a re-charge.
For portable projects I use 3.3V Arduinos exclussivly and power them from 3 or 4 AA NiMh batteries or 3 x AA NiZn. Much safer, no need to thow batteries away if you accidently let them go completly flat.
USB powerbanks, which do normally have an automatic low voltage cutoff, are another good choice.
I'm now super worried that I'm going to blow up a Lipo if I use that! The thought of my project catching fire is not a good one considering where I want to user it!
Is there a safer rechargeable battery that I should use?