What are the best apples for juicing, and which ones should I avoid?
Almost impossible to give a consistent apple, because even some of the most praised apples will vary radically by location and year to year.  Do note though that many cider apples won't hurt you, but are generally not culinary apples as they are far too astringent.  Even within cider apples there are three categories, sharp, bitter and sweet and the best cider often are a combination.  

Some of my personal favorites will be considered poor by others, but I will mention them anyway.  A Northern Spy requires considerable chill, is a huge tree, tends to biannual, and take a long time to produce, but is an old time traditional tart fresh cider apple with nice body and lots of juice.  A newer and popular apple, honey crisp is very juicy, and makes a nice base but I would tend to mix is with something with more body.  Winesap, a great fresh cider apple, but also tends to biannual, is a northern apple and has fallen out of favor.  My personal favorite, Cox Orange Pippin, but it needs to be an English version by this name, the US version is inferior, and it is not cold hardy.  It is however an excellent fresh apple, makes a very good fresh cider and is an apple that makes a nice hard cider even without mixing.  If you are in the wrong environment it simply will not grow though and "real" ones are often difficult to find depending on where you are.  Local extensions are a great source for this though they typically will only test common varieties.

I would suggest though that most important is to find what varieties perform well in your location, it will vary, and know exactly what you want and like, sweet, tart, hard-draft, hard-dry.  Then I would recommend you are on the correct line wanting a mix to build a deeper body.  And do not be afraid of using crabs.  A few crab apples can make all the difference when added to otherwise drab juice.