Question 1: Algebraic skills (instead of fearing a messy expression, be able to plow into it, and work out the details without careless mistakes). Geometric interpretation (be able to take an algebraic expression, e.g., y < x^2, and interpret what it means geometrically, i.e., for the graph).

Question 2: Work toward satisfying 1 and imparting "mathematical independence" and mathematical curiosity.

Question 3: When students arrive technically prepared, mathematically curious, and not fearful of the subject.

Question 4: Appreciation of the need for theory (instead of fear of it), willingness to get their hands dirty (instead of thinking everything must be so simple), excitement for what mathematcis is (instead of boredom), an appreciation of the fact that mathematics is not an assortment of algorithms.

Question 5: Euclidean Geometry. Then the power of calculus. Then the elegance of basic analysis.