Which stats are important when looking at DSL line quality, and what do they mean?

Solution 1:

Brief

You want the Line Attenuation as low as possible and the Signal to Noise Margin as high as possible.

A signal-noise margin of less than ~8dB may be problematic.
Attenuation of above about ~40dB will probably start to limit your speed.

Line Attenuation

Attenuation is how much power / "volume" of the signal is lost between your router and the exchange.

The higher attenuation is the quieter the signal is and the harder it becomes for the router to "hear" correctly.

Is caused by being futher away from the exchange, having a poor microfilter, excessively long extension cables, poor cabling, EM interference, etc.

Signal to Noise Margin

The signal to noise margin is the difference in amplitude between the noise and signal - how much "louder" the signal is compared to the background noise. Very similar to signal to noise ratio (as you mentioned) but is an absolute measurement, not relative.

If this is small it is difficult to tell the signal and noise apart.

True noise is much harder to control (see this Wikipedia article for some info on electrical noise) as "noise" does not technically include interference - but you modem will not be able to tell the difference. So instead check for sources of possible interference - other devices on the phone line, object generating EM interference over your extension leads, poor microfilters, etc.

Solution 2:

Is this a new problem?

High SNR, low attenuation is best. I think the exact specs depend on the type / kind of DSL Modem and DSLAM. Other things that can affect the performance is distance and quality of wiring.

Can you run test from the DEMARC? If so you can isolate if the problem is related to the house wiring. I would also try a new modem / splitter pair.

The obvious, all you are seeing is your end so you would need to talk to the DSL provider to find out what the link looks like from their end.