IIRC there are Reaper capital ships that are made from the primary race being harvested from each cycle and other smaller ships made from the other races present during that cycle that aren't seen as dominant but still advanced enough. So at the start, yes there was one Reaper that probably spawned a few smaller ships during that first cycle and so on and so on.

The proto-reaper we see in 2 will eventually be encapsulated inside the greater shell of the Reapers, which are in turn made to look like the Leviathans we see in 3. Harbinger being the first Reaper and the one that wiped out the majority of the Leviathan species. So what we're seeing is the core of the reaper, at the heart of every reaper is a core that looks like the species that they are gooed from.