I've never done it, likely never will.
By the time you have enough experience for it not to be more than a little suicidal, you'll need to ask all the other questions over again. You need at least two or three (better 5-10) years' solid sailing experience in varying boats, weather, conditions. Then think about it again. There's a reason the Coast Guard requires 2 or 3 years' worth of 8-hour days to sit for even a small captain's license.
Once you've done that, look at what others have sailed, and spent. There's a young man just finishing a 'round the western hemisphere solo voyage in a 27' Albin Vega: http://crabsailing.org/http://crabsailing.org/
That's about as small as you should go, and the Vega's a solid offshore boat, most are not. I think the voyage cost around 25K, and it sounds like this was bare-bones, most will cost more--look up the Laura Dekker and other teenage solo attempts in the recent news, betcha they cost a whole lot more.
Crossing the Atlantic I would guess you average 4 knots (if nothing breaks), 3000 miles so around 30 days, but you don't need us to tell you that.
As a long-term goal? Great. But get the experience, then judge for yourself if you still want to do it.