How about both of you go, and actually read the bloody Kamihime Project thread hmm ?
There is plenty of explanation there.
There are no SSR Kamihime in the pre reg, only SR. There are SSR Eidolons.
Kamihime is a character that you use in the party. An Eidolon is a Summon "monster" you use for special combo power attacks (Like Final Fantasy Summons, or any JRPG for that matter).
On Page 5 and 7 is the list of the best pre reg Kamihime (SR and R). As for the eidolons, anything less than an SSR is not worth it.
Nova Kaiser Dragoon is one of the better ones ( I had the Darkness Dragoon but swapped it for SR Kamihime when I got lucky enough to get one). For the full list, go check the above mentioned pages, it will maybe help you decide which one to keep when you pick them as each of them uses a different element and different strategy.