Project Starseed

My father is a science fiction author, I highly recommend his work.  He asked me, the other week, what would be necessary to actually build and run a generational starship.  As we discussed some of the requirements, a design and mission profile began to emerge.  This is far from complete, by any stretch of the imagination, but an idea formed.  In the future it will be developed further, for now a brief outline:

Tentatively called "Project Starseed" the goal is to scatter a human presence throughout the galaxy as early as possible.  Requirements are therefore put in place that the required technologies cannot be outside what is currently achievable.  Engineering and technical challenges will remain, but these are surmountable.
The project operates in four phases:

Phase 1: A robotic probe is sent to the nearest acceptable star system.  The system must have at least one large gas giant and sizeable rocky remnants.  These are the most common planetary bodies observed in the galaxy to date.  This voyage is expected to take ~35 years.

Phase 2: At the same time as the Phase 1 launch a second vehicle is sent.  This significantly larger vehicle has a crew compliment 500,000 and takes at least twice as long to arrive at its destination.  During this time the population makes use of raw materials to expand their habitat and double the availability of small or intricate components.  The population is expected to approximately double during the 70 year trip to its destination.

Phase 3: On arrival the probe begins using available resources to construct a second Phase 1 probe, an empty Phase 2 vehicle, and fills fuel tanks for two of each spacecraft.  Remaining high carbon containing rock is ground into a dust to be applied to be converted into soil for the agricultural decks of the Phase 2 vehicles.  This phase is expected to take ~35 years.

Phase 4: The Phase 2 vehicle arrives at its destination.  Components requiring human oversight or fabrication are installed into the new vehicles.  Half the crew transfers to the new vehicle.  Two new destination systems are selected and the cycle begins again for each.

This continues until a system is located with a planetary body adequate for human colonization.  At this point the next step begins:

Phase 5:  One vehicle and probe remain in the system at the end of Phase 4.  Introduction of plants and animals and colony construction begin.  This is expected to take ~70 years.  At the end of this phase half the population disembarks at the newly constructed colony while the other half remains with the vehicle, which restarts the cycle at Phase 1.

Although the time scale for colonization is initially slow, the spaceborne population growth accelerates.  Within a few generations project success is virtually guaranteed through shear force of numbers.  Eventually a large number of extrasolar colonies can be expected.