For a starting character, on Average, 6-10 dice. For skills you're specialized in, 12-16 maybe. If you have a lot of armor and a high body (like, playing a troll), you may need 24+ for soak tests.
Now, this is for a standard, average game. Depending on the GM and players, some folks feel that it isn't proper unless characters are twinked and min-maxed to hell and back. In which case, you'll probably be rolling 16+ dice for your core skill tests.
Later on, once you've built up plenty of karma and money and raised up your skills a good deal, it's possible to start needing 20+ on a regular basis for core skills.
Generally speaking, I'm a big fan of Chessex dice, and have a ton of their 16mm (I think) dice, the larger of the two standard sizes. These come in bricks of 12, so I have two bricks that are my standard SR dice (with my Ork Smiley logo as the "6"

).