Hi, it's quite a topic this one, I invite you to GDIY to talk about this, you will have quite a master class there in this respect.
The most critical part is the generator, you won't be able to get any better than you'r generator does because you can't identify what was generator's fault or what was introduced by the DUT. Even so there are quite nice generators, HP classic topology archives some of the best analog generators for low distortion sine waves. You can filter that out then, to get even better numbers, RC filters could be quite linear using NPO caps and decent resistors (avoid tiny SMD and carbon and you are probably good to go)
Once you get pass the generator isn't as tricky, you don't need such low noise floors or THD on your ADC. Once the signal is out of the DUT first thing it will see is a filter, again, some cleverness would make an 8bit ADC enough to measure few ppm of distortion, but converters and processing comes cheap now days. Use a nice filter, a HPF is good enough, you don't have any useful information till 1 octave later than your fundamental so it's easy to get it XdB lower. Those XdB you will win in your dynamic range of the ADC. Then the software will make sure it reads the values at the points of interest.
In my opinion the importance of a very low THD has to do with eliminating the characterization of the distortion, you may be good all day with a 0.1% THD or not, depending on the content. If you have a heavy weight on higher harmonics it get's much more noticeable very fast. If you have 0.00001% THD it doesn't matter where it is, you won't hear it. Adding the noise to the spec reflects the dynamic range of the device, if your input level goes higher your THD+N will increase, if it goes lower too. So you have 0.001% at +7dBu input, if you put +10dBu the distortion will be higher than optimal, if you put +4dBu your S/N ratio will decrease.
Here goes an over simplification of the application of all this. In user grade audio doesn't really matter, the dynamic range of the signal packed in a CD is quite low, not because of the media but culture, the louder the betta, if you listen to Californication (the whole album) converted to 8bit WAV you won't notice a difference, bit more noise between tracks at most, 20dB dynamic range it's all is really used in most records. When working on a production is quite different, the signal in the room may have twice that easily, probably more. A mic preamp would probably round the 90dB dynamic range, but we still want more in later stages, so if we are 10dB higher or lower than the optimal place it won't affect the final result, and we don't need to worry about the level of the signal at each point (which are a lot, really helps). Then the last step is to crunch all into those final 20dB which will take up signal and noise, but we worked which such lower noise and high dynamic range all the way noise doesn't matter at that point. 32bit floating point audio is used for this reason, it doesn't have any more quality than 24bit but it's much easier to work with, you'll never have a peak you won't be able to handle but you are not worried about digital noise floor. Working on 24bits if you are -40dBFS of your peaks your noise may start to suffer on the lower passages once you take the level up again. I'm careful enough to work with 24bits but it's a very good thing for people who isn't.
JS