Initially, Barnard's Star was selected as the target for Daedalus, as there appeared to be evidence for a planetary system. However, more recent re-evaluation of the data suggests that this is not the case, but thanks to ever increasing sensitivity and better detection methods, we can now be certain that many nearby stars have planetary systems. One of the prime candidates would now be the Alpha Centauri system, mainly because it is the closest star the the sun, which would give a flight time of only 38 years, and because one of it's stars is very similar ro the sun.
After launch, the massive first stage would fire for 2 years, consuming 46,000 tons of Deuterium/Helium-3 fuel pellets. The first stage would then be jettisoned, and the second stage would fire for a further 1.8 years, accelerating the ship an its 450 ton payload to around 16% of the speed of light. At this speed, collision with even the smallest particle would be fatal, so the ship is protected by an erosion shield made from Beryllium, weighing 50 tons. Closer to the target system, after around 25 years flight time, observations would begin to refine the targeting of the probes, using the on-board 5m telescopes. These probes would be deployed at intervals from 30 to 36 years into the flight, relaying their findings back to the ship, which would ultimately be transmitted to Earth, using the huge engine bell as a transmitter, powered by large on-board reactors.
Closer to the target, the risk of collision with dust and particles increases, so another shield method would be employed. Flying approximately 200kms ahead of the ship, small robotic spacecraft would create and maintain a cloud of cigarette-smoke particles to intercept any debris.
The ship itself would be equipped with a large array of telescopes, sensors and other experiments to sample every conceivable object that might be encountered. The probes would be similarly equipped, and would even carry sub-probes and their own ion engines to increase the cross range capability and therefore the volume of space that could be investigated. However, at 16% the speed of light, the whole encounter would be over in around 70 hours.