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A few things. by ndtnguy
Be sure the stone is certified. Without a certification, it's just the word of the guy behind the counter on what the grade is, and odds are he's not qualified to grade it.
I agree with a lot of what ACross says below. Brilliant cut is your best bet if you're doing this without guidance. National chains tend to have a very bland selection. They may offer cleanings, but unless you want precisely what they've got, you'll just be getting something you don't like cleaned. Clarity is indeed more important than size.
"White gold" is a myth: it's just silver alloyed with enough gold to inhibit tarnishing. It also goes in and out of fashion, but pure (or "yellow," if we want to be redundant) gold will always look good. Recall that wedding and engagement rings don't count, so to speak, for matching purposes, so don't just go by what her other jewelry is, unless you know it's indicative of a strong preference.
If you want something other than 1) a plain circle or 2) something encrusted with too many ancillary stones, look at estate jewelry shops or sites. You can find some amazing antique pieces with beautiful filigree that is very hard to find new. I tend to think those are a lot prettier than contemporary rings with lots of tiny stones.
Remember that the point is that she will wear the ring, and one with it, for the rest of her life: if the rings rub together over the years, they will wear out. Look for a ring or a matching set in which the engagement and wedding bands do not lie flush against each other all the way around.