Dripping is just putting a few drops of juice directly onto the atomizer (if you have a 3 piece device -- battery, atomizer and mouthpiece). People wither use the blank mouthpieces with no filling or drip tips, which are mouthpieces with bigger holes, when they drip. If you drip 2-3 drops in you get 5-8 big hits before you need to drip again.
Carts are the mouthpieces with filling in them that hold liquid and Cartomizers are the one piece Cart and atomizer combination pieces that come pre-filled or empty so you can fill them yourself.
Which e-cig is best for you depends on what you are looking for. Do you want something that is small and round like a cigarette? Do you want longer battery life? Do you want something that you don't have to fill as often, do you want to drip? How much money do you want to spend? What device are you using now? What are the things you like about what you use now and what would you like to be different or better? There is no real one size fits all answer, but if people know what your needs/wants are they can get closer to giving you options that will help you find your perfect vape (or as close to it as possible).
Hope some of this is useful

. And Welcome!