Items that have a financial or sentimental value, makes this an important question. Our possessions are often very important to most of us.
The short story is if it is porous and moldy it will probably need thrown away. This includes cardboard, carpet, padding, stuffed animals and upholstered furnishings. Mattresses and box springs are on that list.
Most paper products including books will need thrown out once moldy or wet from flooding . For very valuable items such as a family bible, there is an expensive, but effective freeze drying process that can preserve those items.
Small appliances that have been exposed to mold will need replaced. The cost of cleaning some of these items will often exceed the cost of replacement. Failure to clean these can result in recontamination of the home.
Food items that have been in contact or stored in areas with mold should be thrown away.
Materials that have a solid surface such as plastic, glass or metal are easily cleaned and preserved. Soap and water is the simplest cleaning method. A mixture of 1/2 cup of Clorox to a gallon of water is a great way to disinfect the hard surfaced materials. Do not use a higher concentration of Clorox as it can results in injury to people, pets and the items the mixture contacts.
Clothing is readily saved by washing in regular laundry detergent unless the fabric has been damaged. Mold will clean out of cloth material, but damaged clothing is not restored to its original condition by washing.
The paper materials that did not get wet or damp and do not have visible mold or damaged may be preserved with simply HEPA vacuuming.
Appliances that have some mold exposure but have not been under water may be saved with a professional cleaning. The exception can be electronics of appliances that can be damaged by mold. These may require a professional cleaning. Consult a professional about these items. As an example a hard drive may be removed from a computer and salvaged, but could be damaged if the powered on.
Forced air furnaces can distribute mold through an entire home. These need addressed as a part of any mold remediation.
Mold can and will live behind walls. Removal of house wall finishes may be required to get rid of the mold. If you do this work yourself, learn and follow the principals of containment, negative air and air scrubbing.
Any handling of mold contaminated materials should be done with personal protective equipment such as gloves, eye protection and masks.
There are materials used in the construction of homes that will require replacement as opposed to cleaning. Fiberboard is one such example. That material is used in construction as well as in some HVAC ductwork. Insulation is another common example