Disintegrator shredders provide the highest level of security since the paper is reduced to tiny pieces or even powder, but they are very expensive for home use and are not usually necessary for household security.
Pay attention to the amount of paper you are shredding - all shredders only shred a certain quantity of paper at a time.
If you're purchasing a very large shredder, the lid and shred mechanism may be heavy or cumbersome, so look for a side-loading or slide-out basket rather than a unit where you have to lift the top off to empty it.