The Deadelus project is the direction I think we’ll take.
http://news.discovery.com/space/private-spaceflight/tau-zero-project-daedalus-icarus-110119.htm
"Daedalus was to be a two stage spacecraft, with stage one carrying 46,000 tonnes of fuel and stage two carrying 4000 tonnes. After a total boost phase of nearly four years, it would be traveling at its top speed of 12.2 percent the speed of light, and would reach its target (Barnard's Star, located about six light years away) in 50 years."
The problem with such a project, is that within twenty years of launch, the folks back home will have already figured out how to build a craft that far exceeds the speed of the one that's en route.
If they perfect the design, then send it on its way, it would probably overtake the first craft, and maybe even be home before it arrived at its destination.
I think that timescales of half a century will discourage developers and visionaries from embarking on such projects. They well know the pace of discovery, and will probably keep working until they've got a propulsion system that can get a spacecraft to Barnard's Star a whole lot quicker.