I'd start with a simultaneous release of Ultimate Batman and Ultimate Superman. They'd each have a starting six issue arc that establishes the shared setting and their individual philosophies.
Superman would begin with Kent first coming to Metropolis. He's trying to establish himself at the Daily Planet and fight crime at the same time. Bac in Smallville he's dealt with natural disasters but never done the Superboy thing, and the arc would culminate with him deciding to don the costume and facing Lex Luthor. While he's still discovering himself, I wouldn't make the "alien/human" part of his psyche a central conflict. He's comfortable both as Clark Kent and as Superman. Both are exaggerated parts of his psyche, but they're still part of who he is. Lois is in love with Superman, but thinks Clark Kent is a complete doofus. She's not sensitive and she's not soft. She's a hard-nosed, ruthless reporter, who won't let her infatuation with Superman get in the way of discovering who she is. It's not, "Oh! Look at Lois! She's trying to unmask Superman so she can be with him!" Her interest in who he is wholly comes from journalistic acumen. Lex Luthor is THE most influential man in Metropolis. He's a mostly well-minded philanthropist and businessman who's had to do some illegitimate things for the greater good. His first threat isn't Superman, but rather Clark Kent, who gets a whiff of some of Luthor's underhanded dealings. And Kal feels an obligation both as Kent and as Supes to unwravel the corruption. And it's only as this starts to happen that Luthor becomes seriously unhinged and obsessed with Superman.
Ultimate Batman would begin with his return from years of training abroad. He's not the Frank Miller Batman, and I'd never want to go there. While he's intellectually and physically fine tuned, he's socially immature, and this is a large part of his aloofness. The first arc would deal with him facing the syndicated criminal elements of Gotham City - the same monsters that killed his parents, and the arc would end with the genesis of the Joker. Following stories would deal with how the Batman's presence in Gotham is twisting the town, turning it from a cesspool of organized crime into a showcase of bat-**** crazy rogues. Unlike Supes, Bruce isn't comfortable with both sides of his personality. The real Bruce Wayne is introspective and contemplative, almost Zen-like. He likes solitude, study, and discovery. He's a scholar first and foremost. Both of his public personas are intentinally exaggerated parts of his personality, neither of which he's completely comfortable with. The Batman persona is a seriously frightening extension of his fear and his sense of justice. The Bruce Wayne persona he projects is a social butterfly, a personality he's really not comfortable with but recognizes is necessary. Dent, Gordon, and Alfred are the primary supporting characters. Eventually dual romances develop with both Vicky Vale and Catwoman, as his two public personalities become more polarized. Dent's descent into Two-Face will happen fairly late into the book, allowing the question to be posed dramatically - Is Batman doing more harm than good in the city?
I'd keep both characters in their respective cities, using both the cities and the characters are dichotomies. Superman is an outgoing character who projects his genuine self in both personas. Batman is an introvert, who builds these personalities out of a duty to his mission. Gotham and Metropolis begin to shape themselves around the personalities of these two figures.
After the two six-month arcs, I'd introduce Ultimate Wonder Woman and an Ultimate All-Stars title. Ultimate Wonder Woman would deal with an Amazon with an adventurous spirit who ventures out of her home island to discover the world of man. It would be about coming of age. Superman is a hero, Batman is a soldier, but Wonder Woman is a warrior. While Bats and Supes stay in their individual cities, Wonder Woman's book is about exploring the DCU as a whole. She goes on adventures, discovering all sorts of fantastic things and fighting mythical beasts. Her story is about her finding a place in the world.
Ultimate All-Stars would have rotating writers and artists, telling stories about other characters from the DCU in small arcs. A big part of the DCU is the breadth of the world, and these stories would allow us to explore all the corner of the universe, with characters ranging from the big guns like Green Lantern to the small guys like the Question and Animal Man. Depending on the success of these, they could spin out into new books.
But the Triad remains the primary lines. Superman fights big-name cosmic threats like Intergang and alien threats. Batman deals with the street level criminal threat. Wonder Woman deals with gods and monsters - the mythic and magical in the UDCU. Green Lantern would deal with the antastic, deep space element of the universe.
After a few years, the characters would maybe spin off into an Ultimate Justice League.
