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
(due to switching to carbon fiber, high tech parts
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
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.