You should always start with a new deck of cards...after the cards break in (about 10-15 minutes), they will feel GREAT !
Old cards are not good for several reasons:
1) They stick together, so it is too easy to mis-deal 2 cards, etc.
2) Old cards tend to get dog eared and scratched. These scratchs may be used as marks to idenify cards. Sometimes people help the scratching process along by intentionally scratching cards in straegic locations.
One final note:
If you are considering plastic cards because you think they last longer and/or can not be marked...think again.
Plastic cards are actually more dangerious than paper cards because once they are marked or scratched (intentionally or accidentally), the cards will be used for a long time and can be used against people who are not as observent in spotting a marked deck.
BOTTOM LINE: I suggest always starting with a new deck and you will generally be fine

Stick with quality cards like Bees, Bicycles, Aviators, Hoyle, Tally-Ho, etc. NOTE: Casinos use Bees most frequently at blackjack tables, etc.