Well, only limited first-hand experience here -- my first three batches haven't cleared yet -- but here's my understanding:
1. Plenty of people on this list have reported good results with cheap grocery-store juice as long as it doesn't have preservatives in it. Some express preference for unfiltered or fresh-pressed cider.
2. Pasteurized means essentially no wild yeast/bacteria to foul things up, and most agree it won't hurt your final beverage. Some seem like the authenticity, excitement and unpredictability of unpasteurized; many seem to use campden tablets to sterilize the sweet cider about a day before pitching the yeast.
3. You'll get as many answers as posts, I think. I've heard about good results with Montrachet wine yeast (the yeast for the original and much-loved EdWort's Apfelwein), champagne yeast, ale yeasts, hefeweizen yeasts, and of course official cider yeasts. Wine yeasts seem to take longer, produce a drier cider (more complete fermentation of available sugars), but maybe a smoother one; ale yeasts go faster, seem more likely to be messy (overflow of initial, vigorous fermentation) and probably a little sweeter (lower alcohol resistance).
4. I've heard people using grocery-store Mott's (again, no preservatives) and local farm-stand fresh-pressed. It sounds like it just depends on the flavor. Take your pick, or make several one-gallon batches with different juices (and/or yeasts).
I went with three one-gallon batches using the same juice (a cloudy/unfiltered, pale, pasteurized cider I got at a local farm stand) using different yeasts: Lalvin 71B-1122 win yeast, Danstar Nottingham ale yeast, and WLP300 Hefeweizen. So far so good!
Enjoy! I've made beer on and off for years, but there's something about making cider...