Should I wait to get my wisdom teeth removed until I get to basic or get it done now?

Let the military decide. Many get them extracted the first week in training, if they need to be pulled.
Plus, its free.

The time to get your wisdom teeth extracted is when they: (1) are causing you discomfort or (2) affect the alignment of your other teeth.

Your recruiter is trying to make a quota. Hate recruiters. I was the log chief in army recrutimg support center in 1983 to 85