When using ffmpeg to encode an MP4 for general consumption, should I set the profile and IDC level? (-profile:v and -level:v) Should I bother setting them at all? Basically, what is the guidance on setting these properties?

The specific ffmpeg flags I'm referring to are -level:v and -profile:v.

The video is intended for general consumption, direct download (not embedded in a web page). So most users will probably play the video however their device tells them to. I would like to know what's the best practice so that the highest number of users can view it without problems.

This question asks something similar, but it has no answer about these two settings.
Let the encoder set the level automatically. The encoder will have a default profile (High for x264) and higher the profile, better quality for a given bitrate or lower bitrate for a certain quality target. Unless you have compatibility concerns, default High is fine as well.