There are two DVD box sets that contain the Batman movies of Tim Burton and Joel Schumacher - The Batman Legacy and The Batman Motion Picture Anthology. My advice is to see these movies ahead of time, and buy the ones you like individually. I GUARANTEE YOU WON'T WANT TO BUY ALL FOUR MOVIES - unless of course, you're a DVD collector like me, who loves DVD extras. A serious DVD collector will not buy The Batman Legacy - they'll shell out some extra coin to get The Batman Motion Picture Anthology. That box set comes with 18 hours of extras. The Batman Legacy doesn't have any good DVD extras, so movie buffs won't be interested in getting that box set. But if you don't care about DVD extras, and just want to acquire all four films, you may as well get The Batman Legacy.
As a fan of the Batman comics, I can recognize a lot of problems with all four movies. The first two were directed by Tim Burton, and are generally well-liked today. But the last two were directed by Joel Schumacher, and they're generally reviled by everyone. These Batman movies show what happens when a popular series is put in the hands of a director with a completely different vision, who ultimately destroys the series. THAT is the lasting legacy of this series. The series lost a lot of steam after Schumacher made Batman Forever, a movie that alienated a lot of Batman fans. Then Schumacher made Batman & Robin - and the series lost all credibility after that movie came out. In the case of the Harry Potter movies, Chris Columbus (who directed the first two Potter movies) said he wanted to ensure that the next Potter director would not stray too far from the style of his first two movies - and he cited this Batman series as an example of what he hoped to avoid.
Burton's movies are enjoyable - but a little ridiculous. Some of the villains and goons were a bit too cartoonish for my liking in Batman Returns, but they're WAY too cartoonish in the Schumacher movies. However, the character of Batman in Burton's movies is perfect. Batman may be a hero, but the character is so dark and gritty that there's a real malevolence to him. The Kilmer and Clooney Batmen didn't have that malevolence - so viewers won't experience the sense of awe and wonder that Keaton's Batman evoked from them.
Harvey Dent (Billy Dee Williams) is in the first Batman movie. He doesn't turn into Two-Face in this movie. I figure they wanted Dent to appear in this movie with the hope of making him a villain in a future sequel. Williams doesn't add much of anything to this movie - but it would have been AWESOME if Burton had Williams play Two-Face in a Batman sequel. Too bad Two-Face doesn't appear until Batman Forever, when Schumacher took over. Even though Batman Forever is a sequel, Schumacher completely ignores Williams' portrayal of Dent, and cooks up a completely different character for Tommy Lee Jones to play. In a Burton movie, it's safe to say that Williams would be playing a leaner, meaner and less eccentric Two-Face than we saw in Schumacher's movie. The first Batman is also the only movie of the series where the villain's goons are cool - but they would have been cooler if they kept their old fashioned mobster appearance of fedoras and trenchcoats. The goons in Batman Begins are ninjas - and there are few things on Earth that are cooler than ninjas.
Batman Forever was a rude awakening for those of us who expected the Batman series to retain the same style as Burton's movies. Schumacher and the writers didn't know how to make a good Batman movie, and Kilmer was miscast as Batman. Batman didn't deserve the title of 'World's Greatest Detective' in Batman Forever. He should've done some investigating into Nygmatech when he suspected that "the box" could be used for evil purposes. Batman certainly dropped the ball that time. Anyway, Schumacher was trying to make Batman Forever a much more lighthearted film. Then he made the travesty that is Batman and Robin, which is like an updated remake of Batman: The Movie and the Adam West TV series. And for the record, I'm a big fan of the Adam West TV show. That show was a product of its time. But IT'S NOT suitable for this day and age - Schumacher should've known better. But I imagine he was a huge fan of the TV series, and this was probably his way of paying homage to it. Another serious problem with his movies was the way the villains were portrayed. Bane, Poison Ivy, Mr. Freeze, The Riddler, and Two-Face were all too obnoxious and/or annoying for my liking. I expect The Joker to behave like a clown, but TWO-FACE and MR. FREEZE? What was Schumacher thinking?
Let me put it this way. If you loved Batman and/or Batman Returns, you'll probably be able to tolerate Batman Forever, but you'll HATE Batman and Robin. If you love the Adam West TV show, you might like Schumacher's movies. But it's hard to say, because Batman & Robin is a terrible movie, whether you like bright and cheerful superhero movies or not. Fans of the Batman comic books will appreciate Burton's movies, dislike Schumacher's movies, and LOVE Batman Begins - but that movie isn't a part of this Batman series, so it's not in this DVD set.
I myself will be getting the Anthology - I'd LOVE to hear the commentaries from Schumacher. I'm curious to hear what he was thinking as he made those movies. Thank God Batman Begins came along - the start of an entirely NEW Batman series. Now I can forget about Schumacher's movies, and all the problems with Burton's movies. I like Burton's two movies a lot. But Christopher Nolan's NEW BATMAN SERIES will become the best comic book movie series of all-time. Mark my words.