I'm going to be running the Beginner Box for the first time for a few friends. I'm thinking I want to flesh out Otari, but I don't have Troubles In Otari, which I plan to buy and run later. Should I worry about creating conflicting elements of Otari, or is it as sparse on details in the other two APs as it is in the beginner box?
The Player's Guide for Abomination Vaults includes a ton of information about the major players in Otari: https://downloads.paizo.com/AbominationVaults_PlayersGuide.pdf
That said, don't worry too much about contradicting the official lore. This is your game, and if something in the guide contradicts something you made up, just don't present it to your players, they will never be the wiser.
Take a look at the Roseguard section in the pdf though. That should give you an understanding for why this town exists, and informs some of the politics that are currently going on.
If you are planning to run Troubles in Otari later, you should be aware that it consists of three short adventures dealing with the lumber industry, the delivery service, and an abandoned fishing shack just outside of town. If you want to ease your players into these quests, you may want to introduce them earlier.