I hope you know how fortunate you are at 20...you have fifty years of fun and adventure ahead of you! There are many paths to accomplish your dream of sailing the world, however, I believe at your age that the best option is a Maritime Academy. I am a little biased toward Cal Maritime, but if you enroll and earn a Marine Transportation degree, then you will graduate as an Unlimited Third Mate and can find a job immediately.
This is not some 9-5 job where you get weekends and a few weeks to pursue your dream. This job and career puts you out on the water immediately where you will become familiar with safety at sea protocols, electronics and navigation equipment that are non-existent in most small boat scenarios. That's a plus by itself, but what is really nice is that you will be making over 70k/year to start and by the time you upgrade to a Second Mate in a couple years, you will be making over 100k with 4 to 6 months off each year to sail wherever you desire.
CSUM | Academics Â» Marine Transportation
Also, you travel the world while working and get familiar with different seas and locales. While working you don't get much time to explore the exotic ports that you will visit - it's not a cruise ship and you are there to work - but commanding the bridge while steering into places like Shanghai with its massive traffic is something most can't even imagine and will refine your skills when sailing your own yacht.
The one thing that I have found on the big ships is that although you become acquainted with the latest regulations and some top notch equipment, most of the Mates and Captains don't have a clue what it is really like down on the water in a 40 foot sailboat traveling through serious swells and weather. To me, that is real sailing. I wouldn't let 90 percent of them sail my boat 26 miles to Catalina, much less an ocean crossing.
I am starting to ramble, but as an old man who loves and lives on the sea, if I could do it over again then I would go to a Maritime Academy at your age, join a yacht club for some weekend sailing and races to understand small boat ops and actual sailing/sailors, crew on a few regattas, get a 3rd Mate license upon graduation and laugh all the way to the bank and the South Pacific in the sailing yacht of your choice!
It is really that simple.
All the best,