The sweet thing about the GGTS is that it can take virtually any PV battery up to 18mm in width. Personal tastes are about as varied as the selection though.
My personal preference is based on the width of the GGTS. It takes the IMR/High Drain or Protected 18xxx batteries and I prefer them to utilize the width available.
For super short or stealth vaping, you can use the 18350's. They only run about 700mah but they are great for out and about in a palm sized package. For extended use like a road trip, being lazy all day around the house or anything that you may not want to interupt to chage batteries, I like the longest 18650 batteries. Many prefer the IMR for their higher drain scale across the life of the charge. I personally prefer the P or Protected 2600mah ones for a balance between keeping as high a voltage as possible and the additional hours.
My overall favorite though has become the 18500's in either IMR or Protected. I can get most of a day from one and it strikes a great balance as to overall length for me. As to brand, I prefer the AW branded batteries as they have a history of actually supplying a battery that is closer to its rated mah than most others. This is general preference though as the <xxx>Fire batteries are cheaper and some use them with great success.
When choosing between IMR/High Drain versus P/Protected batteries, no battery is "safe" but the IMR uses a generally recognized "safer" chemistry than the P Lithium Ions. The P's have a circuit that is supposed to shut the battery down during thermal runaway but nothing is fail safe including the IMR's. That's why the GG series utilizes vent holes and an upgrade fuse protection that will break the circuit in the event of excess heat.
Never use an unprotected Lithium Ion battery though. Just not worth the risk.
As to chargers, I have had great luck with the Trustfire TR-001 Charger which is cheap (approx $16 USD) and generally reliable. Their model 188 (approx $18-24 USD) is a more advanced charger for very little more and is switchable to charge 3.2 volts as well as 3.7 batteries. For maintstream, the Cadillac is the Pila charger (approx $45-50 USD). It will generally charge the same battery in about half the time (roughly
) as say the TR-001. Whatever charger you get, I can't urge strongly enough to not leave the charger unattended and use it on a fire resistent surface like a bake pan/cookie sheet.
During the charge cycle and on its completion, check the voltages of the batteries (using a Multi-Meter - from $6 USD to ???). When they are completely charged, they should register no higher than 4.2 volts (+/- .01 or so). Batteries are replaceable and cheap as compared to the
rare instances of a thermally challenged battery or one that simply goes out of spec but it can happen. There are threads on ECF dedicated to the pros and cons of each type of battery but like anything else in life, don't allow yourself to be overcome with information overload.
While we drive cars daily and think nothing of it, there are so many things that are inherently dangerous about them that we learn to accept that fact, use common sense and rely on good safety measures and go on our way. The same is true of PV batteries and chargers. In the law suit happy world we live in, it takes 20 lines of caveats that can scare the hell out of you just to answer a basic question.
As with the car, use good common sense, follow common safety measures and enjoy. It doesn't get any better than freshly charged batteries in an Imeo made GGTS!