This week alone has brought a slew a people joining the forums who want to do the same thing and from the limited information you provided, I don't have an idea of your sailing experience and background. Just saying that you have daysailed (for a couple weekends? For the past 20 years?) doesn't say much. I would suggest starting out by cruising this forum. Start with the Liveaboard & Cruising
Spend some time determining where you want to cruise so that you can narrow down the choices of type of boat you will need. Be realistic about your plans. I wonder how many people who want to "sail the world" really get all that far offshore?
While the thought of escaping by boat is great in theory, it's not always the same in practice. Read books by those doing it, ask questions in the forum, get a true idea of what you'll be looking forward to.
If you have the means, I would also consider chartering for a few weeks at a time in different locations. You'll get a better idea of how you'll do "out there" as far as boat handling is concerned as well as get experience on larger boats. Most boats suitable for just daysailing won't be adequate for offshore. Also, different personal skills will be needed as well as different equipment requirements for your boat.
Lots of people will tell you to "just do it" and throw caution to the wind, but I tend to err on the side of my and my crew's safety. The more you know and train for, the better equipped you'll be to deal with the emergency situations that will
arise and therefore have a more pleasant experience.
Take classes so that you are aware of your legal responsibilities, required equipment. Learn how to read the weather and not depend solely on other people's forecasts. I recommend joining Seven Seas Cruising Association
(SSCA) and participating in their webinars and taking advantage of the vast amount of members' offshore experience.
Good luck with your journey towards leaving (it can be just as exciting if you let it) and don't stop learning.