Any of the covers you mentioned (or pretty much any diaper cover out there) will work with prefolds.
Bummis super brite are great - I would get both the nb and small b/c if you go with these the nb is *super* tiny. Those 2 sizes together will have the same fit range as the Thirsties Duo size 1. FWIW the super brite is my favorite cover - I'm currently using them in size medium.
Thirsties Duo size 1 is also a good cover. I didn't have the size 1 when DD was smaller and wish I had (I like the size 2 now).
Flips will likely be too large for a newborn. They are not my favorite covers since I prefer to snappi/fasten my prefolds and they are really more designed for tri-folding.
Bambino Mio will also be fine; I just think they are expensive for what they are - a made in China cover with a very small weight range. So you'll have to size up on covers more frequently than with the Thirsties, Bummis or Flips.
ETA: my favorite cover for the NB period was Proraps classic in newborn. They aren't the prettiest ones out there, but they have a very defined umbilical scoop and nothing ever got through them. Plus the price can't be beat.