this shouldn't be a big issue. It is something that you will have to keep in mind

A shredder is your fist line of defense
against identity thieves. Here are a few tips about what you should
shred, and what to look for in a shredder.

What You Should Shred

We all get all kinds of junk mail, and you never know what kind of
information is in those envelopes unless you look inside. The only time
you should discard a piece of mail before you look at it is if you are
perfectly comfortable putting it through the shredder sight unseen.
Once you have checked out the enclosed materials, you can simply
recycle them if there is no information that an identity thief could
use against you. If there is any personal information at all, however,
put that thing through the shredder.

Any documents containing personal information including bank account
numbers, passwords and PINs, social security numbers, signatures and
credit card statements should be shredded before they are discarded, no
ifs, ands or buts about it. Make a habit of discarding these items via
a shredder and you will greatly reduce your chances of being
victimized.

Buying a Shredder

There are many things to consider before you buy a shredder, but here are some of the main items:

Strip cut vs. Cross cut. The verdict here is in favor of cross
cut, hands down. While a strip cut machine can often handle more papers
at once, the shreds it creates can conceivably be pieces back together
by an identity thief. Not saying it would be easy, just that it is
possible. And in this case, with so many high quality cross cut
machines available at the same price, there is truly no reason to
compromise your security by using a strip cut shredder.

Sheet Capacity. This should only really be a concern for higher
volume users. If you are looking for a shredder to use every couple of
days for short periods of time (say, after receiving your daily
onslaught of junk mail, or paying your credit card bills) then a
machine with a sheet capacity of 6-8 pages per pass should be just fine
for your purposes. Just so long as you stay within the stated capacity
of your machine, you should be able to avoid paper jams and other
messes that can occur.

Continuous vs. Intermittent Duty. Again, for a personal use
machine, this shouldn't be a big issue. It is something that you will
have to keep in mind, however. Personal shredders are only meant to be
used for a relatively short duration (say about 15 minutes) before they
have to be rested in order to prevent overheating. All this means is
that you should take care to use your shredder on an as needed basis
rather than letting your papers pile up and trying to take care of them
all in an hour-long shredding session.

CDs, DVDs, and Credit Cards. An increasing number of shredder
can handle these items and this is a good thing. Personal and
confidential information doesn't just come in paper form any more, and
getting rid of compact discs safely can be a problem. A machine that
shreds credit cards can take the worry out of discarding them as well.