When adopting, is there a wait period that would cause us to have to come back to the shelter or can you go in and adopt when ready?

There is an application approval process. Application is online as well as available at the cat house.

You will need to fill out an application on the website or in person. A volunteer will follow up with you. It takes a few days for the process, but it's worth it.

There is at least a 2 day wait. After you apply, they do a phone interview, and if they need to contact your landlord that can take longer. I would recommend applying and putting down the name(s) of the cat you are interested in so they will "hold" the cat for you pending application approval