I've accumulated several different pieces of gear to measure distortion. I've not become an expert on any of them, but have been spending many hours on most of them to better understand them and use them properly. Here's my take on each:
Amber 3501A: Compact, easy to use, and good for quick measurements such as when testing rebuilt amps, preamps, etc. Not as accurate as some units, but still useful and usually priced pretty well.
Sound Technology 1701A: Huge, but well-built and seems pretty accurate for its age and design. Plenty of settings/features, but probably best purchased if you find a good price.
HP339A: Very accurate, good performing low-distortion oscillator. Very nice quality build and meter. Quick to use when one learns the proper operation. Much more compact than the ST. Important to get a unit in good condition - it's a lot of work to repair these, from what I've seen online.
HP8903B: Going away from analog to digital readouts, and adding some features. Still no longer current, but also very fast to use and get good, accurate readings (or accurate enough for repair/refurb purposes). Prices have risen because they are still very useful, valid instruments. Pete Millet wrote software to automate readings using GPIB. I really like mine, and recent replacement of electrolytic caps and some other maintenance increased accuracy. When I want extra accuracy I use one of my ultra-low distortion oscillators.
EIDA Cosmos ADC and APC: Purported to be extremely low distortion. If you thought the documentation on other gear was sparse, get ready for a Chinese-built unit designed and produced by a Russian engineer. You'll have to either be very familiar with this methodology or find some help online. I've taken some measurements recently and the units do seem to perform very well. They are also affordable, but you need other gear to supplement so the cost adds up. You can use the ADC with a low-distortion oscillator, or buy the APC which is quite good.
Scarlett 4i4: Higher distortion than the Cosmos, but you null out the distortion to a great extent when you create a profile in the software (I'm using REW). About as easy (or not) to use as the Cosmos.
Akitika ultra-low distortion oscillator: Really nice bit of kit for the price, easy to build and use, and very clean signal.
Finally, I have a Pete Millett sound card interface, which seems to have been designed prior to the abundance of good quality USB sound cards and seems to have been designed for internal computer sound cards. It uses a digital display that seems to be unavailable and one of the ICs has become rare and expensive, so while he still sells the face plates and circuit boards on eBay, I'm not sure it's a good choice to try to build now.
Also, I have a KA Electronics ultra low distortion oscillator (balanced or single-ended) and notch filter, and a balanced attenuator. It was easy to build but integrating it into a chassis box with the various inputs, outputs, and switches took me longer to do than building the PCB. Seems to be extremely high performance.
It you are going with sound cards, you do need some sort of attenuator. I've made PCBs for a few different attenuators for use with sound cards and have listed them for sale for cheap here in BT from time to time. I've built several into different boxes for different uses, and they are very compact.