You probably want a Catmull-Rom or similar interpolating (instead of approximating) spline. It's much easier to control animation or other paths when you know it'll precisely go through the points you specify.

You also need to care about velocity when using splines as trajectories. In general, if you sample a spline at a constant delta-t, your speed through the world won't be constant.

This is especially true if you've got large smooth curves with small "sharp" curves that you want to keep a constant speed over. You can mostly just ignore it if all of your curves have a fairly constant curvature, but obviously test first.

I did end up using Hermite curves and letting the designers and animators tune it how they wanted.