One would think that the closest star systems would be the easiest to reach. But unless you are content with a fly-by examination of the star system, with much reduced science returns, you will need to decelerate the probe at the far end, without any infrastructure to assist with the braking.
By combining both light-pressure braking and gravitational slingshots, a team of German, French and Chilean astronomers discover that the brightness of the destination star can significantly increase deceleration, and thus travel time (because higher flight velocities can be used. Sling-shotting around a companion star to lengthen deceleration times can help shed flight velocity to allow capture into a stable orbit.
The 4.37 light year distant binary stars Alpha Centauri A and B could be reached in 75 years from Earth. Covering the 0.24 light year distance to Proxima Centauri depends on arriving at the correct relative orientations of Alpha Centauri A and B in their mutual 80 year orbit for the sling shot to work. Without a companion star, Proxima Centauri can only absorb a final leg velocity of about 1280km/s, so that leg of the trip would take an additional 46 years.
Using the same performance characteristics for the light sail the corresponding duration for an approach to the Sirius system, almost twice as far away (8.58ly), is a mere 68.9 years, making it (and it's white dwarf companion) possibly a more attractive target.
Of course, none of this addresses the question of how to get any data from there to here. Or, indeed, how to manage a project that will last longer than a working lifetime. There are also issues of aiming — the motion of the Alpha Centauri system isn't well-enough known at the moment to achieve the precise manoeuvring needed without course corrections (and so, data transmission from there to here) en route.