Past posts suggest using homebrew when creating a character, but no homebrew options are shown to me, despite having it selected.

In fact, I don't have access to any of the subclasses.

Then you likely only have the free version which doesn't grant subclass access.  Or only bought the physical version, you have to own the digital version to use it with the character creator.

Did you buy the PHB, or is it shared with you in a campaign? If the latter, you must be making the character in the campaign in question.

Also, check your entitlements: 

https://www.dndbeyond.com/account/licenses

I own the digital license