Mediator or Attorneys First?

Which comes first? We have agreed to do this. We don’t know where to start. We want to be frugal because money is a hurdle for splitting up into two homes. We have children and plan for 50/50.

Do we each retain someone first? Then find a mediator?

Do we find a mediator and then branch out to our own attorneys?

Does order matter? Is one method cheaper than the other?

What are good qualities to look for in these professionals or when asking for referrals?