In general, what's the best practice to authenticate a user via 3rd party (say Twitter) using iOS's ACAccountStore and then tie it to an existing user in my own service assuming that they were logged in already? Can I access and store the account credentials remotely over ssl, or is there a better way?
And if they had to re-login via Twitter, I could just search for the user with that twitter handle to know what backend user is tied to this account, yes?
And lastly if I wanted to be able to login via a browser later on, I would get new oauth credentials for the webapp as well, but could search for a user with the same Twitter account info and store these credentials as well, and know that they all refer to the same person, correct?
What you're asking involves many levels of a system "stack" that are custom to a particular environment. What is "correct" vs "incorrect" is dependent upon the environment you've set up and are connecting to from your iOS app.
So from what it sounds like you're leveraging iOS's Twitter functionality to create a Single Sign On (SSO) experience. There are several guides on Twitter's site for doing what you want to accomplish: