if you are talking about filtering the yeast and trub out of beer (and not a filter for brew water) you will be using the filters once and throwing them out- theres no storage. on some retail kits, they say you can filter up to 10 gallons at a time with one cartridge... you might be able to do more or less depending on how much stuff you are filtering out and how quickly the filter gets clogged.
to sanitize, fill the cartridge housing with starsan up to the top, insert your filter and close it up. push some more starsan thru the whole thing using a keg of starsan (or other sanitizer). use CO2 to push the starsan out of the filter. filtering is where you can add a lot of unwanted oxygen to your beer if you arent careful. pushing the sanitizer out with 100% co2 will ensure the housing is 100% oxygen free.
buy a 10 or 25 pack of (non-charcoal; just regular fabric) filters anywhere from 10micron to 50 micron. any smaller and you will just have more clogging issues. smaller than 5 micron starts to strip hop flavor from the beer. any cloth filter is going to absorb some of the hop oils just by virtue of being absorbant. however if you go too small on the micron rating, even more will be removed from the beer. yeast cells are in the range of 30-100+ microns, and hop particles are usually 50+ microns, so theres no need for smaller.
filtering is kind of a pain and has a legnthy procedure that is the same regardless of if you are filtering 2 gallons or 15, so the more beer you can filter at once, the more efficient it will be.