There are a lot of books out there for players to use. Advanced Races, Ultimate Magic, Ultimate combat, etc.
I am playing with all new players to pathfinder in a one shot to give them a taste of what pathfinder is. I will be moving on to the adventure path Carrion Crown when they finish this one shot.
I think the Ultimate books are too powerful personally for level one players, but thats just my opinion.
Is there something in the adventure path informing me of what books are recommended for the path? What books would make things too complicated for complete new players to pathfinder? Should I just stick with the core book?
In my opinion it's not that the later classes and options are too powerful for new players, they just dont need that many options. Unless a player is specifically asking to play a character that you know could be easily represented by a Magus or Slayer just have them use core. However, if they're already accustomed to RPG's and are just new to Pathfinder you could probably get away with opening a few more books.
No, the path doesn't include that kind of recommendation. Pathfinder is designed to more or less work with any of their books (excluding special systems like Mythic or the Technology Guide).
Here are some particularly appropriate books in roughly descending order of importance:
Occult Adventures (especially Kineticist and Spiritualist)
Horror Adventures
Haunted Heroes Handbook
Advanced Class Guide (especially Investigator and Warpriest)
Ultimate Intrigue
Pathfinder Unchained (especially Unchained Rogue, plus Unchained Summoner with a Psychopomp eidolon)
Advanced Race Guide (since Professor Lorrimor traveled a lot, there's more freedom in race selection)
I don't even know what's in Ultimate Magic and Ultimate Combat because they're such defaults.
Some other books that should generally be allowed because they're a big help to martial classes:
Weapon Master's Handbook
Armor Master's Handbook
Personally, in my games I mostly just remove Gunslinger (flavor issues and difficulty balancing enemy AC) and Magus (large burst damage and same-y tactics makes fights repetitive but hard to balance), then toss out some of the stronger metamagic. I work with them to figure out what they want from a character, and try to match it to something as best as I can. Ended up with a Half-Elf Fey Bloodrager and a Tiefling Psychic Investigator.
Personally I would allow all the books, excluding things as you find them rather than banning books in general. Nothing is too powerful really, especially if you have newish players. Maybe ban gunslinger due to flavor, other than that though you should be good