What would be the best type of phone grip for this Case?

OMG, that's sooo huuugee

Serious natural nails right there.

Umm, I think in that case you would probably want to get a simple, subtle ring that can be attached without altering the pink aesthetic too much.

It seems impossible to find a ring that could be installed on that easily that would do that, though, btu I first envision a simple black or silver ring...

An all black pop socket is most likely what would work for you - installed very carefully, of high quality, with a sort of guarantee that it won't come off easily or leak adhesive around it to ruin your pristine pink case.