So, how much ‘current’ do I need? And, is this a rating or spec that is provided?
Don't worry about the current!
What is needed is the power to drive the speaker in such a way that its frequency response is flat and that its loud enough without audible distortion.
These two can be quite different, but the thing to understand is that the current cannot exist without power! There is an immutable law that binds them together. It is Power = Current x Voltage where power is in watts, current in amps and voltage in volts. This law is unlike a speed limit in that it simply cannot be violated without creating a new branch of physics which isn't going to happen with amps and speakers :)
The big deal here is that the amp must be able to act like a voltage source with this speaker. What that means is that over the entire range of impedances expressed by the speaker, the amp must be able to make the same voltage (if a simple sine wave were applied to the input of the amp, and swept over the range of the speaker). This can be done by a tube amp or solid state, as **this ability has more to do with output impedance than it does anything else (like 'current')**. In tube amps a low output impedance is achieved by application of negative feedback. Solid state amps often have a low enough output impedance without feedback, but usually are non-linear without it so they have feedback too with rare exception.
The feedback induces a servo control aspect to the amplifier- the output voltage is fed back into the amp as a correction; this essentially tells the amp to make more power into lower impedances and less into higher impedances.
This comes with a price, like all things in life. Feedback adds distortions of its own when applied to an amp, even while suppressing distortion in the amp. This distortion can be heard in any amplifier as brightness and harshness (since it is composed of higher ordered harmonics to which the ear is keenly sensitive). This is why there are amplifier designs that don't use feedback, and complementary speaker designs that don't expect the amp to be a voltage source.