I wish you the best, but make sure you keep your activities legal. No sense getting a criminal record and ruining your career at the start! Don't hack into any systems you don't have permission to attack. If you want to experiment, do it on your own machines.
As for the biggest problems... there are so many it's hard to pick just a few, but I shall try. First off, the enormous number of poorly managed machines really make things easier for attackers. As the Internet has grown, the average skill level of system administrators has dropped greatly, leaving many systems ripe for the picking by even amateur attackers. Also, the widespread availability of high-speed always-on connections (cable modems and DSL lines) connected to home users' systems helps attackers. It's very easy to undermine these puppies and use them in a distributed attack. Other big problems include the fact that our underlying protocols (TCP/IP) are pretty weak, and the fact that software vendors continue to release broken programs with major security flaws. The fact that we're still discovering buffer overflows on a daily basis in the year 2002 is somewhat depressing!
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This was first published in November 2002