Lowering a car does not change the weight of the car. The higher the spring rates the more bounce you will have. Teins are good because they are similar to shorter stock springs, because they retain the same spring rate as the full size springs. He wanted less bounce, this is step one of how he gets it. Step two has to do with shocks/struts, not his springs.

OP: Springs bounce, that's what they do. Shock absorbers slow down and limit how much springs bounce. Your stock shocks are meant to work within a certain height range, unless you sectioned your struts and shocks when you cut your springs, your shocks are acting like they are partially compressed, meaning they don't do crap. This is why your ride is so bouncy. No matter what springs you have, with your stock shocks you will get bounce unless you get rock-hard springs, in which case you will simply break a tooth every time you hit a pothole.

Brand is less important than quality and function. Look for what is going to get you what you want out of the car. The S-techs are gonna be more on the comfort side with the lowered look, while Eibachs are much more on the handling side. Do some research on spring rates and damper rates, especially if you're not planning on getting adjustable.