A system for cleaning a wellbore can include a bottom hole assembly that is designed to be run downhole into a wellbore after the wellbore has been drilled and before the wellbore has been cleaned. A control sub-assembly is mounted on and carried by the bottom hole assembly. The control sub-assembly is designed to be positioned within the wellbore. Multiple cleaning sub-assemblies are interchangeably mounted on and carried by the bottom hole assembly. Each cleaning sub-assembly is designed to be positioned within the wellbore. The multiple cleaning sub-assemblies include at least two of the following sub-assemblies: a scraping sub-assembly that scrapes an interior of the wellbore, a brushing sub-assembly that brushes the interior of the wellbore, or a magnetic sub-assembly that magnetically captures debris within the wellbore.