If I want to minimize the line current draw of a magnetically ballasted lighting system that uses lag type NPF/LPF ballasts, how can I determine which capacitor capacitance value is appropriate for proper power factor correction?

For example, what capacitor do I need to add in order to enable power factor correction on a 120V 60Hz F20T12 preheat fluorescent tube fixture that draws 380mA using a simple series choke ballast?

You have to first calculate the reactive component of the ballast current and from that the capacitance, then select the nearest lower value available one. All comes from equations:
Total current is
Iballast = sqrt(Ireal^2 + Ireactive^2)
Real power input (you may measure with KillAWatt or so):
Preal = Vmains * Ireal

And the reactive current is
Ireactive = Vmains / Xcap

Capacitor reactance is
Xcap = 1/(C * 2 * Pi * Freq)

So solve those equations and you get the capacitance...

For example, what capacitor do I need to add in order to enable power factor correction on a 120V 60Hz F20T12 preheat fluorescent tube fixture that draws 380mA using a simple series choke ballast?

The problem is that you data is incomplete, you do not know the real power factor of your lamp + ballast system. You can look up it on the nameplate, measure with a watt-meter, or guess. For example, at 120V your circuit will consume 45.6W apparent power. Let's wildly guess the ballast loss is 3W and tube power is really 20W, so by energy conservation law the active power is 23W. Solving power triangle, Q=SQR(S^2-P^2), reactive power to compensate is 39.3W. So, reactive current is 0.328A and the capacitor needed at 120V 60Hz is about 7.25uF. Practical PFC capacitor value is usually a bit lower, full compensation is not achieved.

One serious thing to consider, in the real life lamp/ballast current is not exactly sinewave. So, using simple equations for linear networks in not entirely correct. Fortunately, 100% power factor correction is not needed in practice.

No, but installing a cap to give the best possible PFC makes the ballast run a lot better.