Radio
Radio is easiest considering distances and the issues with moving the patterns of energy we call atoms around the vastness of space. Photons are essentially mass-less, so can only go at light-speed, which makes them very convenient for information transmission.
Radio does have the difficulty that you emit in all directions, effectively wasting most of the signal energy, and potentially making the communication subject to interception and decryption by hostile parties.
Lasers
High energy lasers can maintain beam focus over vast distances. Diffraction will still be an issue at inter-stellar distances, but the energy dilution is much less than that of radio. Transmission of course still occurs at the speed of light.
Cargo-ships
Properly constructed cargo ships (no human crew) can accelerate at tremendous rates and approach $c$ much more quickly than a standard one gee flight plan (by standard I mean accelerate half the journey, decelerate the other half).
$$S = (2c^2/a)\times(cosh((at)/(2c)) - 1)$$
where, a is acceleration, t is (ship) time, S is distance and c is the speed of light. All units are in SI.
So for $\alpha$ Cen, at 4.37 light years away, while a standard 1 gee $9.81 m/s^2$ flight plan would take 3.6 years shipboard time to cover the distance to $\alpha$ Cen AB, a ship capable of 100g acceleration would only take 44 days (ship board time) due to time dilation onboard. Of course, the source and destination are not in accelerated frames, so would measure something higher than 4.3 years in duration for the journey.
Peak cargoship velocity from the home planet reference frame:
$$V= (1 - (1 + aS/2c^2)^{-2})^{1/2}c$$
Peak velocities:
With a one gee flight plan and 3.6 years total (ship-based) flight-time, you get to 0.95c.
With a 100g flight plan and 43 days (ship-based) flight-time, you get to 0.999990c.
Caveat
$\alpha$ Cen is actually a close binary star system, with a more distant 3rd companion, and therefore rather unlikely to have habitable planets in stable orbits in anything like the goldilocks (not to hot, not too cold) range.
Also, with regards to both the 1g and 100g standard flight plan, there is no current known technology that would allow that sort of sustained acceleration, since the energy requirements are astronomical. Of course, this is moot since we're talking about the brave new future.