Cam,
While there are well built boats, and poorly built boats, the type of question you are asking is pretty meaningless...
The best boat I know of, or that has likely ever been designed for heavy
offshore sailing is an open 60 though they are out of your
price range. An open 6.5 would likely be the best blue
water boat in the $60,000 range, but living on a 19 foot boat with two people is rediculous. First you need to define your sailing area, the Carribean or the med have very different requirements than the
south pacific, or north Atlantic.
Frankly too many people start off wanting the best built boat they can, and that isn't a terrible place to start, but every boat is a compromise, and to get that heavy
weather capability costs you a lot somewhere else. Either in speed, which means you will burn a lot more
diesel,
price (due to switching to carbon fiber, high tech
parts,
sails ect), or livability.
For instance if your longest regular crossing is going to be 500nm or less than speed is a major
safety factor. Perhaps even more so than ultimate build quality since a fast boat can make a crossing within a
weather window that a slower boat can't. On the other hand if your average crossing is 1500 miles then speed goes down, but
radio communication goes up, so you can avoid the worst weather. If the nearest safe harbor is less than 100 miles (most of the Carribean) then
shallow draft may be more important to
safety, so you can put in at poorly charted
anchorages easier.
No boat is perfect, and there are a lot of different definitions of safety, and a lot of ways to make a boat 'safer'. Your specific needs determin what will make a boat safe for you, and you need to have a lot more information than has so far been provided.