Yes, get the offer in writing.
And pay attention to how the offer process goes.
A friend of my recently went through a protracted process where the hiring manager would offer, then waffle. They’d talk, then he’d change his mind. They’d agree, then he’d withdraw the offer.
By the time my friend called me, she was frantic. She needed the work and wanted the job.
“What’s it been like going through this process?” I asked my friend.
“I feel jerked around!” she responded. “I don’t trust anything this guy says.”
Consultants have a little saying: As goes the contracting, so goes the contract. (Originally from Peter Block, I think, but all my books are packed right now, so I can’t check.)
I advised my friend to look for other options. I bet offers isn’t the only place this guy waffles.