Insurance claims, bank statements, paid bills, and the like need a home once you've reviewed them. A file cabinet is ideal, but a file box that slips under your desk or onto a bookshelf works fine where space is at a premium. Even a cardboard file box will do, as long as there's a workable file structure inside it.
Write out a list of the statements you get each month (or every two months, or twice a year). As you do, categories for filing will suggest themselves. The key is finding a system that meets your needs and triggers your memory when you're searching for something.
Organize files by broad subjects (though not overly broad; now's the time to strike the word miscellaneous from your vocabulary). Next, create subcategories―say, Medical, divided into BlueCross BlueShield, Dental Insurance, Lab Reports, etc. You might file all financial statements together by month. If your life's less complicated, filing everything alphabetically may do nicely.
Write up labels and alphabetize for quick retrieval.