What do you look for in an advisor?

Hey all, as a very early stage founder, I've been fortunate to have a few very supportive contacts who have been invaluable in brainstorming and providing a listening ear. We haven't yet talked about equity or particular expectations.

At what point do you formalize the relationship? Is it usually on the founders to extend the first offer? Do you have any particular thresholds that you consider (e.g. after X meetings)?

And more generally, what would you want to get out of an advisor?

Thanks and I appreciate your time reading.