I am building a thing that is is run from an nano, it has a servo attached to it the servo needs
Operating voltage of 6.0V
Idle current 8mA
Running current of 450mA
Stall current 2500mA
This device needs a rechargeable power supply one the does not wreck the batteries when the power levels get to low I may run the nano from the same power supply.
I need advice on what type of battery to uses
One option is 6V SLA - go to Vin in the Nano (might be a little marginal to guarantee
the 5V rail is 5.0V), but should be happy to easily handle 2.5A surges to the servos and
is pretty much spot on 6V.
Any battery that struggles with the 2.5A surges won't be a good choice to power both
servo and nano - separate supplies would then be better.
Alternatively if your servo can handle 7.2V I'd go for 5 AA NiMH pack - that's 6.5V or
thereabouts, more overhead, but you'll need to go for good quality cells that happily handle
the current (experimentation might be needed). 2S LiPo would be slightly too high
a voltage (perhaps some diodes in series to drop a volt or so), but would have no
problem with current.
2 LiFePO4 batteries will give you ~6.4V, and should have no trouble with 2.5Amp draw for short periods. I like that they come in a standard AA form factor and therefore it's easy finding battery holders for them.