Oh, cats. I've got a cranky case myself - and I've grown up with cranky cases.
What you're technically SUPPOSED to do, according to most shelters, is to separate the cats completely for a period of time (two weeks to a month, usually - the shelter here recommends two weeks). Don't let them even see each other. They'll smell each other, though, and the idea is to get them both used to each other's smell. Once the "quarantine" is up, then you can let them see one another, but not come in contact - putting up a gate usually works well, and that lasts about two more weeks as well. Then after THAT, you can let them socialize and interact face to face without a barrier.
Personally, I think that's overboard. I just let them socialize and get used to one another as they will, no "quarantine". Lily, my cranky case, is the worst of them, and the most she's ever done in a fit of pique is to start trying to smack one of the others upside the head. (She's declawed, which helps.) She usually just hisses and growls and carries on like the world is ending, which is fine and also kind of hilarious because she has a growl three times her size. I wouldn't even be upset if she did get into a tussle with one of the others unless there was serious bloodshed and screaming going on, and in 26 years of owning cats I've never seen any cat brought into the household be that cranky.
Long story short, you're probably alright, they may never get along but as long as there's no screaming and carrying on - and you will KNOW a pained cat scream when you hear it - it's okay to let them, well, be cats. Also, if you get super worried about fighting, a squirt with a spray bottle can break them up if they get going.
Younger cats will also integrate better than older. *stares at kitten who thinks she rules the house*