The best aproach would be to accelerate continously Reaching relativistic speeds within a few months
Hmmmmmmmm -scratches chin-
Average weight of human, 80 kg.
Let's assume each passenger will need 120 kg of support (renewable food, medicine, etc).
Let's also assume we have 100 humans to start a small colony.
We now have a 20,000 kg spacecraft, which is pretty much the absolute minimum. The kinetic energy of such a ship going at 0.95 c is gonna be ....
KE = m c^2 [(1-v^2/c^2)^(-1/2) - 1] ≈ 2.2 m c^2
≈ 4 * 10^21 Joules
For reference, the *world* energy production in 2008 was 4.7*10^20 Joules.
So it would take the total output of the world's electricity 10 years to accelerate this craft. Double that, actually, since the propellant coming out the back would have to have the same energy going the other way.