The nominal 7.4 volt lipo will be good until the cells are around 3.5 volts (I am very conservative, you can take them down further).
I would try the 7.4 volt pack first, and see if it can power the step downs and give you good voltage to operate you peripherals at the point where you would be stopping the lipo discharge, 7 volts or 6.5, whatever.
If there is insufficient headroom with the 7.4 volt nominal then use the 11.1volt "3s" pack.
I agree the 5 volts for the Arduino should come from a step-down for greatest efficiency, more so at 11.1 than 7.4 volts.
Lipos are amazing. But they do need care. I use naked lipo cells and batteries of them, but I also
- monitor cell voltage carefully when in use
- charge them with a real lipo charger while disconnected from projects they power
You can learn more than you need to know at batteryuniversity.com. At the very least know that lipos can store a huge amount of energy and are quite capable of delivering it rapidly whether that was your intention or not. Sometimes this energy does undesirable things.
Lipos need a little more care and attention.
If you want to have a neat rechargeable device with a build in battery, then yes, I would recommend additional circuitry to manage charge and discharge, which circuitry or module should include all protections.
a7