For store bought juice, just make sure there are no preservatives. Ascorbic acid is fine, nearly all store bought juice will have it. Basically, the acceptable ingredient list is apple juice, apple juice concentrate, water, and ascorbic acid. Don't buy juice with anything else added.
Everyone has their favourite yeast so a read of the sticky at the top of the page (CvilleKevin) should help (and confuse). My current "very favourite" is WLP775 (liqid yeast) but currently I can't get it here in Oz so my fallback is SO4 (dry yeast). I have also tried the "usual suspects" (Nottingham, EC1118, DV10, etc... they all work).
Bought juice can be quite sweet, which goes away during fermentation leaving not much else but acid and tartness, so my best results with bought juice are a base of "tart" juice (say, Granny Smith) plus a bit of sweeter juice (say Pink Lady). But, this all depends on what you can get. Ideally grind and press your own juice but sometimes this isn't practical.
So, read all the posts as they come up... there is a lot of good stuff in there. I mentioned in a recent post that when starting out, people are sometimes disappointed that their cider doesn't taste like a lot of the commercial alco-pop ciders. ( made with concentrate and water, yeast filtered out, sugar added, force carbonated). Most yeast will ferment down to 1.000 or below leaving a quite tart dry cider. I have found that SO4 will stop a bit above 1.000 so you get s some residual sweetness and flavour. Also, slow (time) and low (temperature) is the way to go... 6-12 months does wonders for cider. Adding a bit of sugar or juice then bottling gives a nice petillant mouth feel. So, experiment, experiment, experiment.
Spend $50-$60 on a hydrometer, Jolicoeur, and Lea and have fun.