G'Day Illium, and welcome to CF.
Your plan, your
budget and your time scale all sound pretty well thought out, especially considering your age. i see no reason at all that you can't, in theory, realize those ambitions. I'm not a knee-jerk "go for it" type, but there is something about your post that makes me believe you may actually do what you are dreaming about!
So,
advice from an old fart:
First, tell us where you are now located,and where you would like to be living aboard.
This will certainly influence what we might suggest to you... for instance, living aboard in the
New England winter would be a no-starter for me, but we did so in the
SF bay area without a problem.
Weather does matter, and while some can survive happily on a boat in cold climates, I sure can't!
Tell us a bit more about your other life plans. Do you intend to pursue formal education aiming at a career of some sort, or are you more the type that just digs in and gets a job and learns on the go? That sort of consideration influences how living aboard might
work out for you. For instance, if your
employment requires business dress, life aboard a
small boat becomes more difficult!
Another thing to consider is that in many areas,
live aboard marina accommodations are hard to come by and expensive to maintain. Some
marinas have minimum boat size for liveaboards (silly but true). Living aboard on the hook, or even in a
mooring field when you are employed is a hardship in a great many ways. These impediments can really dig into your plans if not taken into account.
Finally, don't start getting concerned about what specific boat you should buy. Boats are so very personal... what's good for me may very well nauseate you, so our
advice is only vaguely appropriate. What is helpful is to hang out around places where there are lots of boats...
marinas, yacht clubs, that sort of spots. Get to know some active sailors and if possible, active live aboards. One excellent means of gaining access to other yotties is to spend some time in
boatyards. Find some folks who are DIYing some jobs and offer to help... you will gain some friends and you will learn some boat knowledge for free. With the contacts you thus make, getting some sailing time on OPBs (other peoples boats) will help you learn what YOU like and aid your choices when time to buy rolls around. That said, remember that the first boat you buy will almost certainly not be the last, so choosing a type that is common and popular in your area will expedite things when it is time to change boats. Selling is a LOT harder than buying!
Enough blather! Have a think about all this crap, and if you have further questions, fire away... you'll get lots of advice here, some of which may be good!
Good luck, mate
JIm