Stay away from the dwarf shrimp. Amano, ghost, rhino and fan shrimp are safe because they get a bit larger. I don't know what kind you saw but if they are less than 1 inch long, forget it.
Most people recommend bigger shrimp with betta fish; I have dwarf shrimp with my betta; he does occasionally chase them for about 3cm and then he gives up. He'll sit next to the shrimp and let them poke him and he'll get fed up and swim away.
My betta is ok with dwarf shrimp; I wouldn't put any dwarf shrimp in with my girls but my male is ok, so it depends on his personality.
I've been looking at shrimp lately, came across some info that says that when people breed blue shrimp the offspring are not blue. So the color is not natural but nobody seemed to know what it is. The green ones, however, are a natural color.