Well, there have been a few shake-ups in the world of DC lately, but this is actually a pretty good time to jump in. Plus the earlier stories are collected in trades that are pretty easy to get. So if you like Batman, Nightwing, and Superman, you have some really good options.
For Batman, the regular Batman title is really good. Currently, Batman is missing and Commissioner Gordon is filling in in a robotic Bat suit. There is a bit of a mystery as to what's going on with Bruce Wayne and the whole situation is temporary. So worry not, as the Batman you know and love will be back soon. Plus the earlier stories are a lot of fun. You also have Detective Comics, which can be hit or miss. Though it's tied into what's going on in Batman, loosely.
For Nightwing, that's the biggest change. Dick Grayson isn't Nightwing anymore, as a group of villains revealed his secret identity. Though Batman helped him fake his death so that he could help Batman infiltrate a spy organization. So now you have the comic titled Grayson, where Dick Grayson is a spy. It's one of the best comics out there and still pretty early in. So it's easy to catch up.
For Superman, you have Action Comics and Superman, both of which are really good right now. The big shake-up there is something or someone is blocking Superman's powers and his secret identity was revealed to the world. So he's trying to put his life back together. Action comics has been great for a while now. Superman is finally picking up some steam.
The Batman and Superman books launched their stories with issue 41. You don't need to really need to know anything going in, as most of what you need to know is covered in the books. The earlier trades of Batman and Action Comics are well worth checking out. I believe the first arc of Grayson was just collected in a trade as well.
You may also like Batman/Superman. It's not that far along yet and has both characters you like. It seems like some big changes have happened lately, but things usually have a way of leveling off and going back to normal. So just jump in and see what you like. You can always back track from there if you like. It's particularly easy if you like going digital with your comics.
Hope that helps and didn't confuse you