Final answer:
The routes associated with suppository administration are rectum and vagina. For home administration of an antimicrobial for a systemic infection, the oral route is the most appropriate and convenient.
Step-by-step explanation:
The route associated with the administration of a suppository can include the rectum (e.g., a rectal suppository) or the vagina (e.g., a vaginal suppository). These routes of administration are chosen based on the type of medication and the intended effect. Suppositories are designed to melt or dissolve after insertion, allowing the medication to be absorbed into the bloodstream.
Regarding the second question, for the home administration of an antimicrobial to treat a systemic infection, the oral route is typically the most appropriate and convenient option. Intravenous administration would require professional medical oversight, topical medications are for localized treatment on the skin or mucous membranes, and parenteral involves injections that are not as convenient for home use unless specifically instructed by a healthcare provider.