You've probably already purchased something by now, but I'll try to summarize just for the heck of it.
A. As someone else said, the older 1st generation design battery is unregulated and starts at 4.2 volts and after a little usage, goes down to its natural 3.7 voltage. It then stays at 3.7 volts until it approaches discharge. As it approaches discharge, the voltage goes down from 3.7, producing weak vaping, and shortly thereafter, the battery shuts itself off. So immediately after charging, it produces a stronger/hotter vape, but then tones down after a short period of time as the voltage decreases to 3.7 volts. You can get these just about anywhere. I haven't checked in a while, so I don't know who's got the best prices.
B. The 2nd generation design batteries are regulated so that they maintain a constant 3.7 voltage throughout the discharge cycle. With these, the strength/hottness of the vape is constant from the time it's taken off the charger to when it's fully discharged. These don't give you more vape time per charge, just a more constant vape. These were pioneered by Bloog as the Maxx Fusion, but are now available from other sources. NHaler stocks these as "M.F. Style" batteries, but I'm sure there are other vendors. I believe Bloog currently has the best price on these.
C. Both of the above come in 3 lengths, 65mm, 78mm and 102mm, the longer having greater energy capacity. The 65mm length with a cartomizer attached is about the length of an extra long cigarette. I believe the energy capacities are roughly 180-200 mAh, 250-280 mAh, and 320-350 mAh, respectively. The actual capacity varies between manufacturer. I like the longer length since they run longer, but that's a personal preference. Cigeasy sells the "Elite" model which has a capacity of 380 mAh. I haven't tried one so can't attest to it, but it might be a good compromise between a standard and a "fat batt".
D. The "fat batts" are higher energy capacity batteries. Many can run all day without recharging, but their diameter is much greater (~14mm or more) than a "standard battery" which has a diameter of 9mm, so they don't look like a cigarette. Also, unless they come with a 'cone', they can look funny with a standard cartomizer attached. Whether the diameter is a concern or not is obviously personal preference. NHaler sells the IGO which has a capacity of 1100mAh. I'm not sure whether its regulated or not, but from personal experience, I think it might be at least partially regulated. I'm sure there are models from other vendors, but I haven't researched it.
E. All of the above come in both automatic and manual switch versions. The automatics have some sort of pressure or airflow switch to detect when you're drawing and turns the battery on automatically. Earlier automatic versions were "finicky", but many of the kinks have been worked out in newer versions. Particularly, they turn on and off faster, and aren't prone to being accidentally activated by loud noises or wind. The automatics are certainly more convenient, but the downside is that they are more easily destroyed if e-liquid gets inside the battery. This happens if a cartomizer is overfilled or if you drip too zealously. I'm not that careful when filling cartomizers, so I only buy manual batteries, but clearly the choice is personal preference.
Bottom line: I think it's Fat Batt and Manual. Second generation is probably better, but it might be difficult to get conclusive information on that.