I want every character, or atleast most, to be evil in their own way, but the question is, is it a good idea?
Technically speaking all characters should be at least a little evil, because a pure hearted person reads as a boring and annoying loser.
Good. Damn good. It would be a Valhalla, or rather, an Helhalla! The possibilities... just think on them... and do it. If you need inspiration, just watch anything similar to Dawson's Creek.
"The trouble is that we have a bad habit, encouraged by pedants and sophisticates, of considering happiness as something rather stupid. Only pain is intellectual, only evil interesting. This is the treason of the artist: a refusal to admit the banality of evil and the terrible boredom of pain." --Ursula le Guin To the OP, it can work. But nothing will kill interest in your story faster than a conflict where the audience doesn't care who wins. And if every character is equally nasty and unpleasant then you need to ask, why would the audience be invested in any of them? Having some characters have some style or impressive audacity to their evil can be a substitute for actually being someone worth cheering for (after all, it worked for what, 90% of the big TV series of the last decade?).
You have a very valid point here. But not necessarily their evilness needs to manifest in all its splendor at the first moment, nor everyone needs to be tagged as evidently mean. A lot of literature and even TV shows, even cartoons play very well the foundations of duality, and if well most of the stories are as cheesy as any, you never can be so sure in which time a paragon of rectitude will turn into the worst nightmare for his/ her fellow man/woman. By example, Disney's Frollo is a clinical case of the antagonist that began with an act of mercy, and deranged quickly and steady by lust. That very same phenomenon may be applicable into a full scale and broader spectrum if you get the right setup and creativity.
I think it could work, but I also think it could backfire. As someone said above, the audience might not care about them if they're all evil. Perhaps you should try "morally gray" characters. They're not evil, but they're not good either. Like most people, really. I mean, very few of us are evil, but very few of us are "pure good."
So everyone is in it for themselves, take all or die trying sort of story. Go... Go... get to it, Mah Boy.
All ideas are good, but the execution would decide if the book's going to be a success or failure. I can't imagine an interesting story where nobody is at least a little good. I can't imagine them as being interesting. If we take "Silence of the Lambs" as an example, you have DrLecter, who is evil because he's a cold blooded murderer, and Dr Chiltern (person in charge at the facility where Lecter is imprisoned), who was also not a very pleasant character and also cold blooded. You can have a story where the Bad Guy (Lecter) is chased, caught and imprisoned by another Bad Guy (Chiltern), whom you can also make just as evil. But because Chiltern was on the side of the law, he is sort of a Good Guy - he is doing society some good by prosecuting Lecter. So you still end up with the Good Guy-Bad Guy situation and the story won't be much different from the original, even if we completely exclude the Goody Good Lady Clarice Sterling (the detective who solves the main crime in the book). You can go further than that and have a story where evil T-Rex and evil Gigantosaurus go around stomping cities, because they are 100% evil and there's nothing good in them. But that won't be a story, just a series of action scenes.