I'm not a particularly big fan of MA's myself. In fact the only MA's on my charts are of volume, so I'll know what's average.
In practically any discussion of MA's you'll see 20-21, 50-55 and 200 periods mentioned. The 20 day MA I can sort of see, it does represent more or less the number of trading days in a month.
I have no idea where the numbers 50 and 200 came from. Although they are watched by enough market participants that even if they have no intrinsic value in and of themselves. There probably is at least some thing of a self fulfilling prophecy effect.
Personally I would have thought a 60 day MA (approximately one quarter) and 240- 250 day (approximately one year) would have made more sense than 50 or 200. But then 50 and 200 were already in wide spread use long before I started and will likely persist long after I'm done.
As for simple or exponential. Particularly on daily charts I would lean toward the simple MA myself but then I'll admit I'm something of a traditional kinda guy.
As far as what "the street" is looking at, I honestly don't know. I'm guessing there are fewer pros looking at these than you think. And the one's that still do use them are probably the older guys who, out of shear habit if nothing else, probably use simple more than exponential.
In the end I would suggest playing around with various periods as well as types of MA's on the time frames and markets you'll be watching and see what works best for YOUR trading style.
Ultimately that's far more important than what anyone else is doing.