As long as it’s working, don’t worry too much about the digital settings! As long as you stay above “CD quality” (16-bit/44.1kHz) the digital files are beyond the limits of human hearing. The quality is limited by the analog side… The noise on vinyl records limits the analog resolution, and there are limits to the cartridge & preamp can have audible effects/defects/limitations too.
24/96 is overkill for analog vinyl (some argue it’s overkill for anything) but it’s the current pro studio standard and If your hardware supports it, the only downside is larger files.
I was assuming the the PA 2.2 does the A/D conversion and transfers to Audacity, but now I am confused.
That’s correct. USB is digital, so the analog-to-digital conversion is being done by the turntable.
The Music Hall PA 2.2 specs show a max USB output of 24-bit linear PCM and sampling maximum 96 kHz. I setup Audacity for that, but find it also works when set to 32-bit float and 192 kHz sampling! Is Audacity re-sampling the digital out output of the Music Hall PA2.2? I thought this was a bit by bit transfer.
The drivers and Audacity can both resample. The standard windows drivers allow just about any soundcard can record or play 24/196 files regardless of the actual hardware capabilities just as a low-resolution printer can print a high-resolution digital photo. Windows doesn’t tell you that it’s resampling, so you can be recording in “high resolution” with a lower-resolution A/D. (Same thing during playback.)
Audacity (and most audio editors DAWs) work in 32-bit floating point “internally”. There are a couple of technical/processing advantages to floating-point and the conversion from 24-bit integer to 32-bit floating-point is lossless.
Digging deeper into the PA 2.2, the A/D chip it uses a wolfson WM8786 ADC. From it’s data sheet: "Stereo 24-bit multi-bit sigma-delta ADCs are used with digital audio output word lengths of 16 to 32 bits, and sampling rates from 8kHz to 192kHz. The PA2.2 uses a tenor TE7022 24bit/96kHz USB receiver, so maybe that is why the device is limited to 24-bit/96 kHz.
The A/D chip is the main component of the circuit, but it’s only one component. And, then there are drivers.
Audio Host is set to Windows DirectSound, not sure that is right
You can use “whatever works”. WASAPI is the newest protocol, so I’d use it if it works your setup. MME is the oldest.
Recording Device is set to Music Hall PA2.2, shows up there when connected
Good.
P.S.
Just in case your records aren’t in perfect condition… 
Audacity has a Click Removal effect and a Repair effect or you can use the Draw Tool to re-draw the waveform. Or, there are special-purpose vinyl clean-up applications. [u]This page[/u] has a list of several applications and tons of other information about digitizing vinyl.
I have Wave Repair and Wave Corrector. Wave Repair does an audibly perfect job removing most (but not all) clicks & pops, and in the manual mode it only touches the audio where you identify a defect. But, it can take me a full weekend or more to fix-up a digitized LP. Wave Corrector works automatically.