First off, congrats on the decision. It was the scariest one I have ever made, but never has there been one that I was so sure about either.
Secondly, my only experience with buying something at jewelry stores has been with Kay's Jewelers, so keep that in mind when reading this.
What are you thinking for a wedding band? Are you thinking something stand alone or a wrap-around? Keep that in mind when shopping for a engagement ring. As for cheap rings.. I can't help you too much. Unless you find something on sale (read: something they've had too long and want to get rid of it), you aren't going to get anything really big. But there are some nice low karat-weighted rings, so just keep looking around. We found a $1400 ring that we could have gotten on sale for $400 (my wife lost her wedding/engagement ring). But since it didn't turn her crank, we went with another, cheaper, option.
What I did for her engagement ring was pick out the diamond, and then picked out a white gold band and had the jewelers put them together. I wanted a nice rock and white gold, and ended up spending $700. Then when we were to get married, she picked out the wedding band (wrap-around). That was far cheaper, as she had more options to choose from.
As far as re-sizing, that shouldn't be an issue. At least at Kay's, they had a service you paid a one time small amount, and had free re-sizing lifetime as long you take the ring(s) to a Kay's. I would imagine many, if not all, jewelers have the same kind of service. The ring will be off of her hand for about a week, tops, while it is re-sized.
Any other questions, feel free to ask.
Thanks to TheViking88 for the sig!!