just seen this ... and my impression is from a different angle
the answering machines I've seen use a mains power unit for power (mainly) - but have a battery as a standby in case of cuts
so if chuck's right ... chucks right - lithium all the way
if it's just as a standby - all being well it will never actually be used .... so you just need a long lived battery
in which case nip to the supermarket and look at the expiry dates
I got a duracell last week that expires march 2014 (if you don't use it!)