This is becoming a challenge, and the ambiguity is contributing to poor material quality delivery to these recycling and composting facilities that exist behind these colored collection bins. For example, food wrapping paper, if uncontaminated by food are best recycled, but once contaminated by food then are best composted, but if meshed with foil are destined to landfill.
Typically the "sort" rules are developed by the recovery collection companies, and given the backend processing, the rules vary that apply to these simple sorting categories. For example, if no recovery program for cloth exist, and if the composting system is limited to yard trimmings, then cloth which is obviously recyclable or degradable would be destined to landfill.
As a rule of thumb in a commercial setting - a compost bin would receive food waste and labeled degradable food packaging. The recycle bin would receive clean paper, metals, HDPE, and glass. The trash would receive items that cannot go into the aforementioned bins.
The stronger question is can I avoid the purchase that generates such choices to begin with!