I'd recommend you start out by visiting James Baldwin's Boat List
, which has quite a few boats that are available fairly inexpensively.
There are quite a few good boats with proven bluewater passages to their record:
The Southern Cross series of boats is one that comes to mind. Pat Henry and Donna Lange did circumnavigations in a SC31 and SC28 respectively.
The S&S 34 that was just used by Jessica Watson to complete a circumnavigation is another good choice.
The Norsea 27 is another good choice, but a bit smaller than the previously mentioned boats.
There are several Pacific Seacraft designs that might work for you as well.
Be aware that a bluewater capable boat will not be as suitable for liveaboard purposes for many people as a coastal cruiser. Bluewater boats tend to have less interior space than a coastal cruiser of the same LOA. They also tend to be a bit heavier with narrower beam and more space set aside for stowage.
I would highly recommend start out with daysailing and then slowly work your way up to making weekend trips, longer coastal passages and then finally work up to short bluewater passages before taking off for the South Pacific. Cruising the Caribbean for a year or two would be an ideal way to learn to make short bluewater passages.
Aside from the traditional sailing skills, you'll want to learn plumbing, diesel engine maintenance/troubleshooting/repair, gasoline engine maintenance/troubleshooting/repair, electrical system troubleshooting/repair, basic fiberglass repair, and basic rigging skills. These skills are pretty much necessary for a self-sufficient sailor who wants to cruise long-distances, as there are no plumbers et al at sea.
You'll also want to take some courses on navigation and such. There are many places you can take such courses. A good book on navigation, such as Hubbard's Boater's Bowditch, is an essential.
Given your budget, finding a boat that is bluewater capable and in fairly decent shape, you're probably going to want to look at boats in the 26-31' range, rather than the 30-35' range. I'd also recommend setting aside at least 15-20% for refitting, upgrading and modifying any boat you do end up buying.