Regarding rugs, it is best to use non-staining vinyl-backed mats or any rug that is labeled as "colorfast." Area rugs that say "Safe for Use with Hardwoods" should be just fine. You can look at rugs with natural backings, such as cotton, jute, and woven backings.
As is the case for all vinyl floors, rubber and latex mats can sometimes cause staining/discoloration, so it's best to avoid them if possible, although there may be some out there designed for vinyl flooring. In that scenario, you would probably want to contact the manufacturer to make sure that there is no risk of damage to your floor. The plasticizers in rubber (natural latex or petroleum based) are what react and cause the discoloration. These are added to the rubber to keep it stretchy and supple.
Most non-slip pads that are recommended for hardwood floors are a safe choice for vinyl plank. The kind to avoid, which are rarely found these days, are the old plastic mesh type, which have a tendency to leave a residue in hot temperatures. Any kind of foam pad should be fine, however. We have included a link below to some worry-free pads so that when you find a rug you love, you don't have to think about the backing!