But what's the difference between the Twist, the Twist C and the Twist K?
The Twist is the original model. The Twist C (for Cone I think) has an atomizer in multiple parts so cheaper to replace the parts that fail more often. The Twist T uses a 'tank' system. The letter C or T does not refer to the battery, but rather the juice delivery system and atomizer type. The batteries from each model are pretty much interchangeable. The Twist is the VV version of that core battery. And there are many knockoffs and variations, like the Vision Spinner, another VV battery.
So when you buy an Ego-T it comes with a tank, or rather a clearomizer. However, you can then put your choice of cartos, cartotanks, atomizers, clearos, etc on there instead.
If you want to go ego, choose a battery size (100mah = 1 hour rule of thumb), whether you want VV or not, and your initial juice delivery preference, then see if you can save with a kit. If not, buy separately, but don't forget a charger.
Personally, I went Vamo and cartotank instead. I have a small ego as a backup.