I use no chemicals and have no haze. Part of the trick is patience. The cider will clear in time. I pasteurize my juice not by boiling but only raise to 160F for about 10 minutes. Very effective and you won’t lose so much aromatics either. Yeast is a matter of preference. ANY yeast will work fine. My favorite is Cote des Blancs which is a white wine yeast which throws off some sulfur over the first couple weeks but the result afterward is very clean and allows all the apple flavor to shine. I like to leave my cider alone for at least 6-8 weeks to ferment out completely (patience!), then bottle with a little xylitol which tastes just like sugar but does not ferment. Works really well. If you do not want to use xylitol, your cider will still be good but very dry and tart. To maximize sweetness in this case, you can try a very low attenuating yeast such as a Scottish ale yeast or Windsor, those will drop out quicker and result in a more balanced cider with no chemicals necessary.
There are other methods but these are my favorites. Cheers!