I'm a big Batman reader, and I'm especially a fan of reading it in TPBs and Hardcovers. Here are my thoughts and recommendations - feel free to ask questions, or PM me for more details.
ESSENTIAL SUGGESTIONS
-"Detective," "Death and the City," and "Private Casebook" - available in TPB (the last one in HC as well), these collect Paul Dini's run on "Detective Comics." Dini is a MASTER of the Batman comic short story (1- and 2-part stories), and is responsible for Batman: The Animated Series. You can't go wrong with these. The first two are quite hard to find, but be patient - you'll see them on Ebay once in a while.
-"Heart of Hush" - the good sequel to Hush, again written by Paul Dini. If you like Dini and you liked Hush, no reason you won't like this. Available in HC and TPB.
-Brian Azzarello's "Joker" - available in HC, featuring beautiful, stunning art (much of it painted!) by Lee Bermejo and great characterization. More Nolan-esque than most Batman books. If you like this, you can see more of Azzarello's "realistic" take on Gotham in "Batman: Broken City."
-"The Man Who Laughs" - available in TPB or HC, it's a modern telling of Batman and the Joker's first confrontation. A sequel to "Year One."
-"Gotham Central" - collected in 5 TPBs (or 4 HCs), Gotham Central focuses on the cops in Gotham. Batman's a guest star, as are his villains - but if that doesn't bother you, you'll get a pretty realistic and a very fascinating look at Gotham, told by Brubaker and Rucka, two modern-day comic writing giants. An incredible set of books, which also happen to feature the greatest Joker story ever told. Art is often reminiscent of "Year One." My favorite Batman series.
-"Prey" - featuring the modern-day telling of Batman vs Hugo Strange, this is another sequel to "Year One." Great art and a fun read. It can be hard to find - sometimes you'll see the TPB go for 30 or 40 bucks on Ebay, but be patient and you might find one for 5 bucks used at a comic store or convention (or even online).
-"Batman and Robin: Batman Reborn" and "Batman and Robin: Batman vs. Robin" - most of the modern-day Grant Morrison Batman is crap, but these two books are real exceptions. In HC or TPB, it's ____ Grayson as Batman, with a new Robin. Punchy, flashy, and fun, I think they are enjoyable as standalone, apart from the main Morrison Batman RIP storyline.
-"Streets of Gotham" - more Paul Dini goodness, but this time focusing on the new ____ Grayson as Batman. Dini's still great, though, so it's a lot of fun. HC or TPB.
-"Batman: Year 100" - The Dark Knight Returns is a sci-fi telling of the return of Batman, in the future. This is a lot like that, but different enough that it stands on its own as well. TPB.
-"Batman: Evolution" - a mix of gritty crime drama and Ra's al Ghul, with a unique color scheme. Really nice little book. TPB, should be easy to find.
-"Batman: Faces" is another neat little book, by Matt Wagner. TPB, it's still in print and shouldn't be too hard to find.
OVERRATED
-"Haunted Knight" - the weakest of the Tim Sale/Jeph Loeb trilogy. I would avoid it for now, and save your money for better books. You can always pick it up later.
-"Death in the Family" - actually, most fans hate this book. Not very well-written, its importance is in its place in history - the death of Robin.
-"Venom" and "Gothic" - they're OK, and largely unmemorable. Like others, save em for later when you've already spent your money on the better ones.
-"Bruce Wayne: Murderer" and "Bruce Wayne: Fugitive" - this story was really long and drawn out and wasn't very good. Way overrated.
-"Contagion" and "Legacy" - really not so memorable or great (though Legacy is a bit better than Contagion).
-Anything by Grant Morrison in the past 5 years or so is crap (like Batman RIP, The Black Glove, etc), except what I posted above.
-"The Cult" - ugh. Avoid this one.
You mentioned looking at "Catwoman: When in Rome." While it's certainly a fun read, Batman's not in it - it's strictly a Catwoman story, and not a very essential one at that. You might be better off picking up other books first.
Others have mentioned "KnightQuest." That's the 2nd part of the "Knight" trilogy (Knightfall and KnightsEnd being the others), but it was never collected in trade, so you'll only read those books if you scour comic book shops for back issues (of which there are like 40). Funnily enough, I just finished collecting all of them last weekend (and I'm preparing to bind them into my own hardbound collection).
It's a real pity, because without KnightQuest, readers don't know how Knightfall and KnightsEnd connect - and it doesn't make sense. (Bane breaks Batman's back in Knightfall, and suddenly shows up healed and ready to fight at the beginning of KnightsEnd - doesn't make sense if you don't read the middle part, but you can't unless you have the back issues).
That being said, Knightfall is alright for what it is - a tale of Batman vs a bunch of his villains, followed by his defeat at the hands of Bane. Like most crossovers, not the best storytelling - but fun for what it is.
"Tales of the Demon" collects the 70s stories introducing Ra's al Ghul. They're kind of interesting from a historical point of view, but be warned that you'll be reading old stuff, from back when storytelling in comics was much simpler and less engaging. If you like modern, sophisticated storytelling, you won't like this one much.
I like "No Man's Land," but it's a bit polarizing in the fanbase. 5 volumes, following Gotham City as it is abandoned by the Federal Government after an earthquake. A ballsy, gutsy move on the part of the editors - the one crossover that was creatively worthwhile. But just be warned, you won't be getting your normal Batman stories here - this is an extended, post-apocalyptic Batman story.
"Under the Hood" is often derided, but if you accept the conceit (that it tells the story of Jason Todd's return), it's not half bad.
"Batman/Deathblow: After the Fire" is one fewer people have read. Brian Azzarello writes, Lee Bermejo does the art (like in "Joker"). It's a team-up/crossover book, but don't let that stop you. Great art and an interesting story. I didn't know who "Deathblow" was, but I still found it a pretty enjoyable book. Can be hard to find, though.
"Shaman" is not bad, but hard to find. An immediate sequel to Year One, but it doesn't feature any flashy, recognizable villains.