Best practices for buying some furniture from the outgoing tenant of the apartment I'm going to move into?

I’m moving into an apartment next month, and the landlord gave me the current tenant’s email address and phone number so I can contact her about possibly buying a few pieces of furniture from her. I don’t have much experience buying or selling things informally like this, so I was wondering if anyone has suggestions for best practices.

I have photographs of the place with her furniture to jog my memory about what’s there, so I know what I want to buy. What I’m unsure about is how to set the prices, what form of payment to use, how to arrange this so we’re both confident we’re actually going to get what we bargained for, etc.

The landlord has said it’s fine for us to do this as long as we let them know which stuff I’ve bought so they know to leave it there. This is in Manhattan.