Color is important because it's something you can see with your naked eye. The scale starts at D and goes to Z. Beyond Z, the diamond is considered a fancy color and it starts to get more valuable again. The majority of engagement ring diamonds are between D and J. D, E, and F are considered colorless. G, H, I, and J are near colorless.
The difference between D and J is obvious to the naked eye, but you can tell when comparing two diamonds. To us, the sweet spot for color and value is somewhere between the two, but seeing them in person is the best way to decide.
If quality is important to you, D, E, and F are great places to be on the scale. If size is really important and the budget doesn't allow for what she's dreaming of, then I, J, or even lower can become options. Yellow or rose gold can help to hide the color.