We're building a site where users will have profile and the ability to post and share pieces of writing. A forum will be a big piece of the site but we're trying to find a package that will allow us to easily integrate the existing user profiles and carry sessions into the forum without having to re-authenticate. Is miniBB good for this? If not, do you have any recommendations?

I don't know about other forum systems, but I'm sure miniBB can handle such kind of tasks in 99% of cases. I'm myself have implemented a lot of integrations for our customers, and they all work well. You just need to be sure your current users table has autoincremental integer ID field, which miniBB will be tied with. All other stuff can be additionally configured. Take a look at our synchronization guide or Paid Support section - we're providing such kind of custom implementations for the fee starting from just US $55.