Hi and welcome
The board takes cca 50mA from 3.6-3.8V, and Li-Po generally keeps useful voltage down to 80-85% discharge, so you can expect to get playing time of [capacity in mAh * 0.8 / 50] which would be around 20 hours for 1200mAh. I haven't yet got to test full discharge curve with Li-Po, only with 2xAAA, so this is only a guesstimate.
Yes the PCB is smaller, 53x25mm, keypad adds a bit, it's 55x28mm and 10.5mm vertically (without buttons).
Actually, it's all here:
http://phonicbloom.com/diy/make_your_own_enclosure/images/keypad_dimensions.pngThe charging circuit is set to max charging current of 500mA to not overload common USB ports, and cut-off is 4.20V which is compatible with Li-Po or Li-Ion chemistry. You can expect charging times in ballpark of [battery capacity / 500] so e.g. 2 and half hours for 1200mAh cell.
For safety reasons, it's perhaps better to have a smaller capacity cell in. When choosing Li-Po, make sure you get one with internal protective circuit (overdischarge and overcurrent). It is very important also to protect the battery itself as Glo board contains voltage booster that will happily continue draining nearly discharged Li-Po (<2.5V) which is likely to damage it.
So, perhaps 1200mAh isn't too much of an overkill, but it really does not make sense to put in any larger... unless you are also adding some external circuitry (more sensors, controls, lights...) for minimal setup, even 250mAh might be fine for daily use.
