I can only comment on the Ultra Fire 10440 3.6V 500mAh for the GG Slim. Actually, mine are labelled 600mAh. There aren't many alternatives - Janty (iVapour) sell them in 350 mAh, and a few outlets sell no-name ones at 320mAh (incl. smokejuice). I have read that all varieties are actually around the 320 - 350mAh range but do not know if this is true.
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Edit>> The DX website actually states for the new protected 10440:
"Product print '600mAh', the exact capacity is 350mAh"
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They also come with TW 510 passthroughs. Ebay as well, though usually only sellers in China.
The batteries are around 4.1V fully charged, and cease to work in the Slim at around 2.8V. I believe this is good as you do not want to over-discharge them much below this anyway. I'm getting maybe an hour or two out of a battery but I tend to vape pretty much constantly when I do, and also deplete the battery faster as I like to let the vapour warm up by keeping the button pressed a lot longer. More occasional
vaping should make it last a lot longer. You may want to invest in a few more spare batteries though, I'd hate to run out of power if I was away from a charger.
I have yet to test the Janty batteries, but haven't noticed any difference between the Ultrafire/no-name ones.
I use an Ultrafire WF-138 charger, there is some debate as to whether it is protected as some are labelled as such and others aren't - mine isn't). I take care with the charger and hopefully there won't be any problems. I can also charge the batteries in the TW 510 passthrough.