I've been doing vinyl transfers for years...I started out doing computer recording with a PSAudio Vinyl Convertor that I had borrowed from work, it worked well..but, it was too expensive for me to keep.
I ended up with a Behringer UMC202HD. I have found that the recordings I have made compare favorably with what came from the PSAudio device.
I tried all kinds of freeware programs but all of them left me frustrated and sometimes confused...I finally settled on Vinyl Studio, which has been the greatest upgrade over the much more difficult to master Audacity, which I thought sucked...VS has many functions that make vinyl "ripping" easier, more convenient especially in noise reduction, track splitting, and tagging...
Your choppiness and distortion could be related to the input level into your interface, the UMC has level controls to prevent input overloading and Vinyl Studio has controls to adjust levels so that you have some actual dynamic range in your recordings vs. what you showed in your screenshot of the recorded signal, which looks like it is maxed out and clipping...
I have the UMC in the tape loop of my preamp and use the preamp's phono section to feed it...I mostly make 24/192 WAV files as you can always down-res files to fit on to portable devices, but you can't increase resolution for better playback quality on better systems....
I bought one of those book sized little computers from Amazon years ago for about $150 and have that connected to the 55" TV in the den as a display...I have a Topping E30Mk2 Lite DAC and the Behringer connected via USB to this computer...I can sit on the couch with a wireless keyboard/touchpad combo and control everything making vinyl transfers a much more enjoyable experience...I basically listen to an album while it is being recorded, after setting the input levels and recording levels, of course,
Then I go into VS and make all the noise corrections, track splitting, and tagging.
It did take me a while to get to that point as I started with a stand alone Pioneer CD reorder that eventually died and was limited to 16/44 recording, plus you had to insert track breaks as you were making the recordings, otherwise it was a lot like using a cassette deck...