It does depend on what you mean by rapier; Meyer calls his weapon a rapier, but WMAists tend to call it 'sidesword'. The impression I get is that Meyer's stuff is based on the Italian, but thoroughly Germanized. Jake Norwood would probably know. Stefan Dieke at Freifechter focuses on that style. One source claimed that he was taught by Marozzo, though this is dubious.
There are several rapier manuals in English. There is the Elizabethan translation of DiGrassi, which is generally considered 'sidesword.' Saviolo is Italian or Spanish-Italian, depending who you ask. Swetnam is pretty distinctive, and probably qualifies as properly English. Pallas Armata I don't know enough about to say.
Spanish style involves holding your blade outstretched pointing straight at your opponent, stepping around in a circle, and doing tricksy stuff to him. It actually uses quite a lot of cutting as well as thrusting. Its theory is heavily based on abtruse geometry and philosophy. There is an article about it
here. Italian has a couple of different branches, IIRC. It's not my bag, but there is a Bolognese style and a... not-Bolognese style?
Anyway, good luck, it is a fascinating subject.
Cheers