I have an inexpensive Royal cross-cut that makes fairly small fragments. I feed one sheet at a time most of the time, but it'll take two or three without complaining much. An earlier unit of the same type broke a gear tooth when I tried stuffing too much through it at once.
Why everyone needs a shredder:
Those people who pick through your trash every week for aluminum cans etc.: they may be getting paid "rewards" by identity-theft rings for bringing in things such as your utility bills and credit card bills and so on. You don't want to find out the hard way.
Why cross-cut:
Because strip-cut shredders aren't secure enough, the strips can be re-assembled to read the information.
What's the best shredder available:
Anything that has "NSA/CSS" certification. Yes, the National Security Agency certifies shredders that are suitable for destroying classified material. These machines make very small particles indeed, like the size of the squares that came out of the old computer punch cards. Very nice, but expensive.
Most of us will have to make do with the best office-grade cross cut shredder we can find. Best = smallest particle size. Some of the cheaper machines such as the Royal have the smallest particle sizes for a reasonable price; the tradeoff is they take fewer sheets at a time. That's an acceptable tradeoff since you're usually not shredding a whole bunch of stuff at once.
If you have to dispose of expired credit cards, feed those through one at a time, or get a machine designed to take them. Just cutting them up with scissors isn't enough. There are small inexpensive credit card shredders that take one at a time and are strip cut; what to do with those is take the strips and run them through the other direction so they get cut into squares. And mix thoroughly with the rest of your household refuse.
What else to do, to discourage identity theft trash-pickers:
Make a thick mix of flour and water, or cornstarch and water, or an egg that's past it's prime, and pour it over the refuse in your bin. It doesn't take much to do the job adequately, and it shouldn't be enough that it pools up in the bottom of your bin. This will make a sticky icky coating that will tend to make trash pickers stop digging any further. What I'd really like to see is something that consists of a motion detector and a water spray nozzle, with a timer. While your bin is sitting at the curb, if someone gets near it, they get a good soaking to chase them away. The timer would click off early in the morning so when the sanitation crew comes along they can empty the bin without getting soaked.