TITLE: How much classical geometry must a geometer know?
QUESTION [9 upvotes]: From my reading Wikipedia, I understand there are several branches of classical geometry (if the ordering is off, or I'm missing a few things, let me know):

Absolute


Euclidean
Non-Euclidean


Spherical
Hyperbolic


Projective


Affine

Transformational
Inversive

These can be studied from:

Coordinate geometry (aka algebraic) view
Axiomatic (aka synthetic) view
Analytic view

The combination of these branches and points of view generate many possible avenues of study. 


How many of these are useful for a modern geometer to know? By useful, I    mean fairly likely to lend intuitive insights into their
  work (This may     seem vague without specifying what kind of work
  they do. But since most     geometers aren't working in classical
  geometry, I guess the work of any     such geometer could be
  considered relevant to the question). 
How deeply must they learn?


I've got a good high school level knowledge of math, and some college level math, and I have an interest in pure mathematics for a career.
EDIT: Added tags relating to modern branches of geometry, so that these kinds of geometers see this question.

REPLY [8 votes]: If you are planning to do research in modern geometry, pretty much nothing on your list is relevant. Instead:

If you are planning to work in algebraic geometry, you should learn commutative algebra or/and complex differential geometry.
If you are planning to work in Riemannian geometry, most likely you should spend time learning differential equations, functional analysis, Sobolev spaces, etc. 

I know, this sounds a bit sad, but the reality is that you have only that much time. I do not mean that learning "classical" geometry is waste of time, not at all, but you have to prioritize...