There are lots of discussions about building spaceships which accelerate at just one G (or less), and approach light speed in a reasonable time. Problem seems how much fuel is required to maintain that acceleration that long; remember, it takes rockets a starting load of around a million pounds of fuel just to push a few G for a few minutes. After that first push, spacecraft just coast (taking clever advantage of orbital/gravity mechanics for further acceleration).
“Problem seems how much fuel is required to maintain that acceleration that long”
With our current understanding of physics the best way to get to the stars would be an array of solar powered lasers on the moon. They would be focused on light sails of a space craft. The craft could then steadily accelerate to a significant portion of light speed.