I may be miss-remembering, but:
The Citadel had the processing facility to convert organic life into new Reapers. With the Collector base destroyed/disabled and no other processing facilities seen in game, the Citadel was necessary to start the harvesting process in the current cycle.
As to why the Reapers started with Earth, this was likely a desire to remove a troublesome species from the cycle early in the war. Humanity in general, and Shepard in particular, showed an adaptability and tenaciousness not present in the other advanced species of the current cycle. This would have put them high on the priority list to harvest and preserve.
The below video has Anderson and Shepard speculating about a new Reaper being made on the Citadel (starting at 1:07).
ANDERSON: I'm in a dark hallway. Reminds me of your description of the Collector base.
SHEPARD: Makes sense.
ANDERSON: You think they're making the Reaper here?
SHEPARD: Sure. They round them up on Earth, then send the people up here to be processed.
ANDERSON: Goddamn abomination.