The filter will act from 30 Hz down. There’s no audio there, but rumble from the record, from the turntable motor and bearing.
A 24 dB rolloff is the steepness of the filter. Back in analog days, 6 or 12 was usually the choice. 18 or 24 was much harder. In the digital world, it doesn’t matter.
What it means is that at half the cut-off frequency, the signal will be 24 dB lower. So 30 Hz is -3 dB, 15 Hz is -24 dB and lower frequencies are even lower level. A typical steep rumble filter.
And why does the cutoff go in the 1000s? When would that ever be used (obviously not for vinyl recording, but still)
There are low-pass and high-pass filters. A typical example of the high-pass is the rumble filter that eliminates almost everything under 30 Hz. A typical low-pass filter is an FM-radio filter, that passes everything under 15 KHz because typical FM stereo radio doesn’t allow for anything higher.
Obviously, for a low-pass filter, you need to set the cut-off high enough or you’ll cut away almost everything. That’s a quite common mistake. I always have to think about the meaning of low-pass and high-pass. It doesn’t compute easiliy 
Always try to prevent the signal from entering the preamp if you can.
I don’t know the rumble filter on the ART, but usually these guys know what they’re doing, so I presume it’s an analog filter at the input. If no mess goes in, the preamp can use it’s entire dynamic range for the music. And analog filters can be pretty clean too, if not to steep and well-designed.
While digital filters mostly are very clean, the preamp (microphone or RIAA) is your main worry. It’s limited in a lot of ways and nothing should be wasted. Once you’re up to line level, or in the digital realm, you can waste all you like. At that level, signal-to-noise ratio and distortion can be forgotten.
A mic or RIAA preamp has to be able to take a 1 millivolt signal to 1,000 millivolt, ideally. That’s a lot of gain. And doing that without hissing and puffing, can’t be done by a lot of the lesser preamps. If you feed those a good signal, it’ll work. But if you feed those a weak signal, polluted with rumble and noise, they will add noise and distortion and what comes out isn’t usable anymore.