TITLE: Varieties as an introduction to algebraic geometry / How do professional algebraic geometers think about varieties 
QUESTION [24 upvotes]: This really is two questions, but they are kind of related so I would like to ask them at the same time.
Question 1:
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. 
Question 2:
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.

REPLY [3 votes]: I don't seem to have the option to edit my answer, but I wanted to correct myself: it is the scheme structure of the limit that determines the possible nearby varieties in the family, not vice versa.  The question of whether the nearby varieties determine the limit is that of Hausdorfness of the parameter space.  One has to restrict the nature of the possible limits to get uniqueness of the limit.  This arises in deciding just how complicated the limit should be when trying to construct a nice compactification of a given family of nice varieties.  It is a wonderful fact that for smooth curves one can compactify them without introducing non varieties.  All one needs is some simple singular curves.  This was first noticed by Alan Mayer and David Mumford in their talks at the Woods Hole conference 1964, whose notes appear on James Milne's webpage at Michigan, (and mine at UGA).  I am roy smith, and have been using mathwonk as alias for so many years online I have forgotten it is not my name.  Is it sufficient to register and add it to my profile, or do I need to sign posts here as roy smith?  That would apparently unlink me from all my mathwonk activity so far.