How much will different brands of EUB strings cost? I mean, do they go from $50-$300 or something like that? I am pretty sure they are more expensive than BG strings
go to www.lemurmusic.com and www.quinnviolins.com I'm not an EUB player but I understand that they use standard DB strings which are, as you have surmised, much more expensive than BG strings. The type of string you get depends on what you want to do with it - pizz, arco or both. Check the archives here for lots of string discussions.
Piezos sense physical vibrations so string material shouldn't have a direct effect (unlike a magnetic pickup which senses the movement of a metallic string through a magnetic field and therefore couldn't get a signal from gut strings and might have trouble with synthetic core strings).