The camera in your phone is almost certainly pretty decent - use that. (Don't use a laptop, resolution is unlikely to be high enough)
Set it to the highest resolution and frame rate available. On many phones, the default will shoot in not-quite real-time and result in video that drifts ahead of the song audio.
Film in landscape. (Portrait looks meh, is hard to edit with and restricts options later on.)
Make sure your face is in the shot. (With decent cameras we can zoom in later, we can't zoom out.)
Think about what's in the background - if it's possible to change the angle for a more interesting background shot, do it.
Think about what you're wearing. (Not just fashion choice, but how the color will contrast with what's behind and around you.)
Make sure there's plenty of light in the room. (Dark rooms will trash the resolution of your video even with high quality camera.)
Make sure the light is not creating shadows on your face or instrument.
Set the camera up and record yourself, then check the shot and adjust for the things above until you're happy.
Set the camera recording, then do multiple takes of the song until you're happy with one. (This avoids having to start and stop the video every time, and you know it's always the last one when you snip the file to only send the actual take.)