Which Digital Level Gauge to buy?

A machinists level is much more accurate than anything mentioned here. For instance, a very low cost Starrett 98-6 level (less than $100) has divisions that are approximately 80-90 seconds or .005" per foot (0.42mm per meter). An electronic level that reads to 1/10 of a degree is reading to 360 seconds.

If you need a level for something that is non-suspended, a machinists level is the way to go.

The phone apps are probably unbelievably inaccurate.

I would like to clarify a point that I had intended to put in my previous post.

If your digital level that reads to 1/10 degree is reading 0.0, you are most likely not at 0.0. You are hovering somewhere between the two points where the level display jumps to +0.1 or -0.1. Depending on when the display changes, you could have around a whole 1/10 of a degree of movement the whole time you think you're at 0.0.

True audiofool nerviosa.

Says a guy who uses a $1500 diamond scale to set up a tonearm :)

By all means, stick with what you're using if you're happy with it. I merely gave another option that's more accurate and less expensive than the fence post level mentioned by the OP.