First, watch a lot of dystopian movies to get into the mood. I recommend 1984, Brazil, Equilibrium, and Gattaca for starters. Next, decide how you want to run your Straight game: players against each other, or against the world.

While it is tempting to arrange all of your players to be from opposing secret societies, that tends to devolve into Classic solutions to problems, especially if your players are familiar with Paranoia and have some "bad habits". Far better to have them belong to societies that are friendly to each other or with complementary goals, and have service groups provide more of the rivalries between characters. I find Straight games are more fulfilling and run a lot longer if the players are devoting their time to improving their positions and showing up their opponents rather than constantly going for their lasers. Straight characters should fear for and value their lives and not want to throw them away blindly. Remember, MemoMax transfers can go wrong, so why pin your hopes on a successful cloning when you can be subtle and careful and get yourself promoted to Green clearance while still on your first clone?

For a fantastic Straight module that can be easily stretched into a mini campaign, I highly recommend the "WMD" supplement. It has a mission for each playstyle, and the Straight mission is one of the best pieces of writing I've ever seen. Rather than denying the pc's at every turn, it awards them for their cleverness and greed, and lets them dig themselves deeper into trouble at each stage. Where most Paranoia missions center around weird and wacky characters and incidents and exist mostly as an excuse for troubleshooters to shoot each other for a couple of hours until the few survivors are killed during the debriefing, this one gives them a real long term job with rewards and consequences, and lets them feel like the masters of their own fates. Give them power, give them more choices than they've ever had in their lives... then make them pay for it.