I believe you buy the engagement ring which is typically a ring with some sort of diamond(s). The wedding ring (aka BAND) is usually just that a band, it can have embedded diamonds or none at all. You don't HAVE to buy the band yourself it can be split... because you have to get your band too. I'm not sure there are 'rules' on who pays for what band.

As for the proposing part- use your imagination, make it meanigful. If she's anything like what you describe it's not about the WHAT you do when you ask... it's about how you asked.