The State of Michigan maintains a watch list of invasives (plants and animals).
Invasive species on the watch list have been identified as posing an immediate or potential threat to Michigan's economy, environment or human health. These species either have never been confirmed in the wild in Michigan or have a limited known distribution.
Prioritizing weeds is a process that is highly site specific. Is the site pristine or disturbed? A remnant or a reconstruction? What is the soil type? Is the site open or shaded? Are there rare species on site and specific weeds that may impact that individual species? Answers to these and other questions will modify the order in which you prioritize control efforts. That said, what follows is a rough sense of the potential impact various invasives may have on native habitats.