What kind of onboard audio does your PC have to offer? That may very well turn out to be good enough (assuming there's a line-in which should generally be the case). It's not like you need a studio-grade ADC to adequately record vinyl, and onboard chips and their implementations have become pretty good. If the digital filter seems questionable, just record at the highest sample rate supported and resample later to anywhere from 96 to 44.1 kHz if need be. (I think you want at least 96k for better click/pop identification anyway.)
Also note that Realtek drivers seem to default to a +6 dB input gain, so a bit more headroom could be unlocked if you find you're running into clipping on peaks. (This may be because the microphone input on some chips like the ALC897 clips soon after reaching -6 dBFS, though this should be of no concern with the line-in.)
Access old input device properties from the system sound settings in Windows, where you can toggle level slider number fields between % and dB display. (Avoid input gains of <0 dB.)
The recording setup I'd use is
Technics --> short RCA cable --> NAD phono MM in, tape out --> RCA to 3.5 mm cable --> onboard line-in.
Best positioning of turntable and preamp is arguably back-to-back, but if you can stack then without any extra hum, that's fine too.
The DAC would only see use for monitoring and playback.
Monitor on headphones and avoid bumps and vibration. Something like a concrete slab on halved tennis balls underneath may provide the necessary isolation if need be. (The first-gen SL-1300 is not a subchassis player yet, apparently.)
Clean records extremely well, consider wet playing. Check strobo for speed accuracy at each side. The user-accessible pitch pots and their trimpot counterparts (plus speed selector) should have been previously cleaned so that they operate smoothly and without dropouts. Unstable speed only on 45 may be an indication of some recapping action being needed. (TL;DR: Turntable and records should be in tip-top shape.)
Also, always check whether the record in question can be bought in digital form with sensible mastering levels and such. Ripping vinyl is a slow and tedious task at the best of times.