Stochastics were one of the first indicators I fell in love with when I first started trading. It's a beautiful indicator in hindsight. You look at it and say, "wow, every time it crosses 20band from 0, the price goes up. Look there, the price went down, and wow, stochastics just crossed back under 80 band!"
Then you try using it in real time, and the results are somewhat different. Yeah, for sure, you get to catch some amazing reversals every now and then, and it's pretty useful in oscillating markets. Of course, as anyone who's tried it will tell you, you get absolutely slaughtered relying upon it when the market trends.
From my own experience, I think a big danger in attaching yourself to stochastics (especially if you've had initial success with them) is that you'll soon begin to see every dip as "oversold" and every rally as "overbought". Why is this dangerous? Well, I'll paraphrase I quote I read on these boards and say, "the market can remain overbought (oversold) for a lot longer than you can remain solvent."
I personally found, after trying indicator after indicator, (and the heart ache and anguish that comes with picking tops and bottoms) that the only really consistent way to make money in the market is by going with the trend and having a "feel" for the market you trade. (Successful bottom pickers, and I know you're out there, feel free to flame me.)
Also, after trading and looking at stochastics for long enough, I think you can have a pretty accurate idea of where the stochastic would be at without even having it there.
I know this doesn't answer your question regarding which length stochastics are best for particular styles, but they're such a "pet hate" of mine I had to chip in with my .02.
Given that there is some "contorversy" about what exactly what constitutes a "scalper" as opposed to and "intra day swinger", I think it would be better if you defined the styles for us as you understand them. The simple answer though would probably be, for scalping use a very short length stochastic (or depending on how you scalp, don't use one at all!) and lengthen it as your time horizon/profit objectives broaden.
As for what indicator to use along with stochastics, I would recommend using any trend following indicator, to give some "counter balance".
Daniel