I am not a female but thought I would add my two cents to all this.
In my humble opinion its necessary to have a ring only because it symbolizes true intent. The fact that you went to a counter… Picked something out… spent a modest sum of cash… and thought hard about all of this… all means to her that you are serious. Woman have heard many “promises” and other BS in their lives. A ring, no matter the size, shows honest intent. It is the intent that matters most… And a plus one carat colorless helps too :P.
Secondly, the sentimentaly value that they will attach to this will surprise you. My girl has thought that she lost a necklace that I gave to her in the early stages of our relationship. Its cheap.. nothing expensive… But she has gone beserk looking for it because of the sentimental value that she attached to it. I told her don’t worry about losing it I’ll buy you something better… But no… She wants that because it was one of the first things I gave her.
Besides… What’s the big deal about giving her the ring… She will be going to the supermarket the rest of her life for you… I hate the supermarket… This is a good trade for me!