Wow, it sounds like a big dream-- but one that can become reality!
Here are some things I found doing open-ocean passage
The winds are, on average, stronger away from shore. We had Beaufort
Force 9 gales crossing the Atlantic, and those are not considered survival storm conditions. Take a look at the Beaufort
scale, especially the wave heights and conditions for a given wind
speed-- because that scale is accurate.
In a displacement
boat in open ocean, you can spend quite a lot of time doing "hull speed." That's as fast as a displacement
boat can go, no matter how it's engineered, so having a high performance boat that can handle light winds isn't as important as having a sturdy, comfortable vessel that can handle rough conditions.
Things invariably break at sea. Learn as much as you can about boat repair, and carry plenty of spares of everything. Part of the joy of "blue water
cruising" is getting off the tourist track, into those idyllic, palm-shaded coves. But those coves don't usually come with state-of-the-art boat repair facilities.
experience sounds fun and exciting, but it's not much like the blue water
cruising life. There are a lot of ways you can get experience "gunk-holing" before you set sail across the sea. Sailing in the Great Lakes
sounds like a good way to start. You might also consider a "bareboat" charter vacation
in some exotic location. (For those who don't know the term, "bareboats" aren't bare at all. They're equipped with everything you might possibly need for a sail-- except a professional crew.)
Finally, about that boat budget-- good news. The best blue water cruising boats aren't the high performance ones that cost megabucks.
So, all in all, it sounds like your dream is doable. The most important thing is to have fun-- or at least excitement!-- at each step along the way.