1. Are there any other stories I should read? I heard Hush was good.
Hush is just a big, bold and brash Summer Blockbuster of a story, without any real substance. It's just a big excuse to throw all of Batman's big villains and allies into one story as well as art from Jim Lee. As a starting point for Batman, it's a decent story.
Dark Knight Returns
(the only story where crazy-***, psycho, *******it Batman actually works) and Batman: Year One
are essential for any comic-book reader. I'd even go as far as to say that they're essential reading for people who can read. Go and buy them right now.
Batman: The Killing Joke
and The Man Who Laughs
are both great Joker stories and worth getting into as well.
Also, if you're feeling up for some Silver Age camp-action, but you want it to actually be somewhat dark and enjoyable, Batman: Strange Apparitions is worth checking out. It's not exactly a story-arc, it's just the run of the Steve Englehart and Marshall Rogers on Batman's books back in the seventies. It reads exactly like a Marvel title with all of the flashbacks and introspective monologues Batman has, not to mention the relatable, real-life relationship problems he experiences with Silver St. Cloud.
Also, if you're up for some novel-reading (you know, the ones without pictures) you should definitely check out the novelisations to Batman Forever
and Batman Begins
. The novelisation of Forever is great because it shows how great the film could have been without the crappiness Schumacher brought to it. The novelisation for Begins is just an even better version of a perfect film. It goes deeper into Bruce's travels and also delves deeper into how he became the world's greatest detective as well as just being an urban crimefighter. Both feature quite possibly the definitive version of Batman; a dark tortured hero, who fights for justice and not revenge, but who constantly walks the line between the two. The novelisation for Begins is even written by Denny O'Neil (arguably the best Batman writer ever) and the novelisation for Forever is written by Peter David (easily the best guy at adapting films into books).
2. If I go to the comic book store, would I be able to just start reading Batman, or does it have a storyline I need to look up?
Good question. The thing about Batman (and most of DC comics) is that it doesn't run in one, long real-timeish
continuity the way Marvel does. It usually just has several story arcs a year that can be read in any order you like. It should be easy enough to just pick up a Batman book and enjoy it.