I am not sure what he means by that statement, it isn't true, the points do not need to be equidistant from one another. I'm not sure what you mean by a curve that doubles back on itself, but Catmull-Rom is local in that if you have multiple points on your spline, if you move the 4th point, it will not affect the curve anywhere but with the lines that are attached to that point. I'm not that familiar with legrange, but I'm guessing moving one point would require a recalculation of the entire curve?

(This has a nice interactive example: http://www.ibiblio.org/e-notes/Splines/cardinal.html)

I would also go with Catmull-Rom. Its a cubic interpolation curve that is connected of more Hermite curves. I think its similar to Lagrange curve. You can get the same Lagrange curve by manipulating coefficients.

Bezier curve does not pass trough all of control points or nodes. But if you choose to go with it maybe it would be better to go with B-Splines instead or with NURBS (Non-Uniform Rational Splines)