US_returnee,

I prefer having both together :), but ask your to be wife. In case you buy both of them make sure both of them are cute and small.
Normally wedding band is simple gold/dimond round ring ( at least mero jamana ma :p), which you put first and then engagement ring is normally diamond which you put after the wedding band.

But again its your choice...and her wish..I don't think its compulsary to get both.

Hope this helps