This. Best thing to do is jump in head first, and if you need some background info, just check wikipedia. I find that they often have surprisingly good articles on comics.
So, first thing you should know is that DC continuity is an ever-shifting landscape and not something to worry too much about. Read what you enjoy and don't put too much thought into getting stuff that "matters" or "connects" with other stuff. As you go along and learn more, things will put themselves together.
And, in some cases, a new creative team will come on a book that keeps its continuity, but they'll take it in a completely different direction to the point it might as well be a brand new version of the character, despite the fact that the previous stuff "still happened".
I'd suggest picking a few characters you're interested in, and then starting with the New52's first issues. As you go along and figure out what you like, you can then work backwards and find the "greatest hits" to broaden your horizons. If you're interested in Batman, try Scott Snyder's Batman #1 from the New52 (Batman has several books going at a time, but that's the main one). Likewise, if you're curious about Superman, try Grant Morrison's Action Comics #1 from the New52. Most everyone else only has one book a piece, so figuring out where to start wont be hard.
As for Infinite Crisis....that's a story from the previous continuity and has no bearing on what's happening now. It was a big, line-wide Event that brought in tons of characters and built off tons of stuff that had been going on for ages (in some cases as much as 25 years or so). I dont think I'd recommend it for a beginner. However, if you're curious about that, you should start with a miniseries called "Identity Crisis" by Meltzer. It uses a lot of characters from across the DCU, most of whom you won't recognize. But it's a character focused story and might be a good way to get your feet wet with these big Events, and what happens in that story leads to Infinite Crisis so if you do end up checking it out you'll have a little more understanding of where things are at. A word of warning however; that story (Identity Crisis) is fairly polarizing. Some love it, some hate it, and it does delve into some pretty grotesque, adult material. If you're on the younger side you might want to skip it.