The manual says the unit comes with a 2 amp fuse, so that would be the absolute max current draw.
At 2 amps, I'd expect the self-discharge of most wet cell batteries to come into play at longer life expectancies.
In other words, that low of a current draw implies you could use pretty much any 12 volt battery and get a day's use out of it. Motorcycle, tractor/garden, auto; don't think it really matters.
And I don't think you'd need a deep cycle battery unless you really plan on running the battery down to near-nothing a lot. Normal starting battery will do fine (especially since it doesn't sound like you'll be using it for anything but the unit.)