What time control can be best used as an improvement tool?

It depends, I suppose. For example, if you're learning some opening and already made some work on theoretical stuff, blitz can be a good decision to let you feel the opening with your hands. But, in general, the slower the better indeed, as someone above said. I'll be honest, the thought of playing classical online doesn't motivate me much but rapid (10+5 I think) may be a good option.
And yes, what can be said for sure, those scary hyperbullet time controls (like 0,25+0) are definitely absolutely useless for one's chess improving. This throwing pieces already has little to do with chess (though it may be funny at times, not gonna lie, but speaking about any positive effect... no).

To improve speed, use 5 minutes or less.
To improve deep calculations, use 30 minutes or more.
10 to 15 minute games are a good balance of speed and thinking !

Do timed puzzles as well for pattern recognition.
Select your BEST candidate move to improve your chances of winning; always DOUBLE CHECK before moving a piece !!!
Attack multiple pieces at once; your opponent might blunder.
Defend as best as you can.
Never give up :-)