Really, if you want to cross inter-stellar space in any kind of reasonable time - O(human lifetime) - you need to go faster. Possible solutions are: solar sail or new kinds of ion thruster. Both of these impart a very small force (and hence acceleration) for an exceedingly long time, resulting in very high velocities. Your target speed is about 10% of c. In the case of the solar sail it receives momentum from sun for ~ 50% of distance (assuming similar-sized star to our sun), and then is braked by the momentum from the target star for the rest of the journey.
Problem with solar sail is it needs to be GIGANTIC, and composed of materials stronger and lighter than those available today. Additionally force from sunlight is proportional to 1/r^2 so your acceleration decreases with distance.
So, nuclear powered ion thruster is probably the answer. But, obviously, this kind of project is expensive. And either way, you need living quarters for an entire society to live and reproduce.