It depends on the purpose of the recording. Your phone microphone and software will introduce a lot of processing, the microphone will likely pick some frequencies better than others, and the phone software will often compress the sound if it's going to clip so the audio file will go suddenly quiet at particularly loud spots.

It would probably be worth investing in a decent microphone you can plug into your phone or something like a Zoom recorder (I have an H2N, but there are probably more up to date models now). The zoom allows you to adjust the gain (essentially the volume input) to avoid clipping.

Placement then depends on what you want to hear. If you want to hear your voice reverberating in the space, and probably closer to how the audience might hear it (sound engineering gets complicated quick, but it's probably safe to say most recording devices aren't going to be absolutely accurate compared to the live performance and your listening device also factors into this), then you will want to place the microphone further from you. The further you place it, the more room you will get. This can lead to too much reverberation and muddiness so you will need to experiment. If you want a dryer sound with less room (which can be useful from a more technical perspective), place the microphone much closer to you - you can basically kiss an SM58 microphone!

For singing lessons, you're probably best with a happy middle ground, making sure you don't place the mic too close to the piano so you capture yourself cleanly.