Don’t forget that power = voltage x current and so a 12V 5Ah battery will store (as-near-as-damnit) the same amount of energy as a 6V 11Ah. Nominally, 60Wh for the 12V vs 66Wh for the 6V. As Ollie says, the ignition is self-generating and really the battery is only used if you want to be able to have the lights on or charge your phone whilst the engine is stopped.
Anyway, I use 12V 7Ah sealed lead acid (SLA) batteries on all my 12V bikes, like the ones sold for burglar alarms, etc. They are spill-proof, can theoretically be mounted in any orientation and are physically much smaller per Ah than a wet battery. Even with the Powerdynamo regulator and coil mounted there as well as a 12V 7Ah battery, I have a decent-sized space for tools, etc. in the battery box on my Supa 5.
I have been told by someone much more knowledgeable than me that the fairly crude charging regulation found on motorcycles is less than ideal for an SLA battery’s lifespan, but in practice I seem to get a good couple of years out of one and, when they can be bought on eBay for £15, that’s good enough for me! Another advantage is that, if you shop around online for a good price, it seems they can be sent in the post, ready to go, unlike wet batteries these days.