In the world of Shadowrun you'll be rolling more dice than most RPG games -- though happily all of those dice are going to be six-sided dice. For Shadowrun 4th edition it's probably safe to assume that you want somewhere between 12 and 25 Shadowrun dice for most situations. The exact number you'll be using really depends on how heavily you managed to min-max your character, and how many penalties you're taking in your actions.
The two common solutions for Shadowrun dice is either to get a couple 12d6 dice sets, or one of the 36d6 dice cubes. The dice cubes give you the advantage of immediately having all the Shadowrun dice that you'll need, unfortunately the dice cubes use 12mm dice, which are very significantly smaller than standard dice. The advantage of the 12d6 dice sets for Shadowrun is that you'll get standard sized 16mm dice. Better yet, when using 12d6 sets for your Shadowrun dice, you can grab them in two different colors, which can help to get a better sense of just how many dice you have when you're gathering them up to roll.
Whichever route you go for your Shadowrun dice, you'll find them here at Awesome Dice!