As far as Masters goes, I just signed a few forms releasing the program and the resort from liability if I was injured.
NASTAR is an excellent introduction to ski racing. However, there are large differences between your average (at the local level) NASTAR course and Masters courses. Masters courses are generally faster, steeper, and more technical than NASTAR courses. This is because in NASTAR there are 5 yr olds slowplowing on the same course that adult racers use. And don't think that the average Masters course is as tough as it gets- I watched the Alaska Juniors race on a GS course that had me plain scared.
Another option is town, club, or coin- operated races. If Masters or NASTAR isn't available at you local hill, they might have one of these options. The resort website might have information or links to clubs in the area that sponsor these events.
I didn't grow up with a ski racing background, which pretty much puts me out of Olympic contention. My family made 3 or so trips a year to resorts on the east coast, usually averaging 9 ski days a year. I raced in NASTAR races back in the '70s when I was rather new to skiing, and was the only one of my cousins never to medal (my snowplow technique wasn't refined). After high school, I stopped skiing for about 12 years. Picking it back up a few years ago, I started racing in an intramural league and found I enjoyed running gates. This year I started winning most of the races and was stagnating (big fish/small pond), so I decided to give Masters a try. Boy, was that an eye-opener! A visiting member of the Austrian ski team beat me by over 8 seconds a run! Video of the races showed just how ungraceful I skied compared to the rest. I finished in the middle of my age class, which did help to soothe my bruised ego. In addition, the support of the group and advice of the coaches improved my times and increased my resolve to participate next year. Man, do I regret missing all of those training days this year! Training was what I was looking for, and the races were my first lesson- gear and fancy wax doesn't win races- technique does.
Running gates over and over again will improve your times, but you'll plateau. Whatever racing outlet you use, take full advantage of the available training opportunities. Coaches can tailor the lesson to your abilities and desires. Books and video lessons can help you improve, but lack the feedback that speeds up progress.