Multicoating applies to any glass you put between your subject and your sensor. Basically, glass is coated with microscopic layers of other material which are designed to prevent reflection at the glass-air interface. Each layer is carefully tuned, and the cumulative effect can be significant. It controls reflections and reduces backscatter which can lead to flare and loss of contrast. Better grades of multicoating on filters also generally go along with better (more uniform and plane parallel) glass. So the good brands/types are B+W's MRC multicoated filters, Heliopan's SH-PMC multicoated filters and Hoya's S-HMC filters.
There are a number of types of filters.
UV is used by many of us for protection against flying debris or small animals/children. It's avoided by many others because they fear it will adversely affect the images they capture.
Circular polarizers are used to control reflections off any non-metallic objects. They work on water, glass, glossy paint, atmospheric particles, shiny hair . . . You will need to rotate the filter for the desired effect. If your lenses (like your 18-55 and 55-250) have rotating front elements, focusing will cause the filter to turn along with the front element, so you'll have to readjust the filter after focusing
