The 4 C's. Cut, Clarity, Color, Carat. You care about them in that order. Carat is the weight of the stone. It's the least important on how shiny it is.
Diamonds are best when they're shiny. Get the best CUT you can. Clarity is next. You can go "VS1" or "VS2" and still be clean to the naked eye, do that. Color is nice, but unless it's directly next to another stone of a higher or lesser quality it's going to look white. Carat is weight. (You can say it's size I guess, but it's not that simple) I've heard a half carat or less is much easier to cut and make look sparkly, so a half carat or under will be cheaper. I've also heard it said if you're going for less than $5k get a solitaire, single stone ring. Over $5k you can get a 3 stone ring or different setting.
Diamonds come in all kinds of fancy shapes now. You DO need to know what shape she likes.
I did not follow that 3 month salary rule when I proposed. Nor did I follow it when I upgraded my wife's ring 10.5 years later. I was happy with the ring both times. I like this one much more though. Better cut.