Alpha Centauri—our first target for interstellar probes?

With the completion of New Horizons' Pluto fly-by, its primary mission, should we now set our sights even higher, ambitiously taking aim at other star systems? If so, Alpha Centauri would probably be considered as the best target for an interstellar spacecraft due to its "proximity" to Earth. This system, consisting of three stars and possible planetary companions, is the nearest to the solar system, located "only" about 4.3 light years from the sun. The problem is that getting there within a hu