The battery killer would be using an LR Atty if you did, which you are probably not on that unit, the trio is a small 280 mAh Batt I believe, your adapters do not fit it because it is not a 510/801/901 and you dont have the correct adapter, they are out there and I do have some.
mAh = Milliamps Hour (mAh) is important because it's the easiest way to distinguish the strength or capacity of a battery. The higher the mAh, the longer the battery will last. Batteries with different mAh ratings are interchangeable. If your battery is rechargeable then the mAh rating is how long the battery will last per charge.
Milliamps Hour is 1/1000th of a Amp Hour, so a 1000mAh = 1.0Ah
Think of a cars gas tank. Voltage is how much gas is being used, and mAh is the size of the gas tank. The bigger the gas tank (mAh) rating the longer the device will run. If your battery is rechargeable, then think of the gas tank as refillable (rechargeable).
As far as Attys go you can run any reg Atty on your Trio, the ones it comes with or any other with the proper adapter. As far as should you get the biggest baddest battery out there, well it depends on what your needs and wants are. PM me and I will fill you in on a couple of the finer things in the ecig world to help you out so you get on track, I will ask you what those wants and needs are for you then make the best recommendations I can to get you there, whether it is an Ego, Box Mod, variable Voltage Mod, Leo, Provari, or try the best I can to make you a satisfied vaping guru putting out plumes of great vapor ok