This really is two questions, but they are kind of related so I would like to ask them at the same time.
In a question asked by Amitesh Datta, BCnrd commented that it is important to learn about varieties in a classical sense before learning about modern algebraic geometry because it is where much of the intuition in the subject comes from.
I was hoping to get some opinions on how much one should learn about varieties (in the sense of chapter 1 of Mumford's red book) before moving onto more modern formulations of algebraic geometry.
Is one meant to gain a rudimentary understanding of varieties and then start learning about schemes, OR is one meant to have a really good understanding of abstract varieties before learning about schemes.
Do professional algebraic geometers think about varieties from a scheme theoretic perspective or from a classical perspective.
This is a seriously soft question, so I will make it community wiki. I am however half expecting it to be closed.