First of all CONGRATULATIONS!!!
For diamonds, it's the 4 c's. Color, cut, clarity and carat.
Color - A diamond of highest quality is pure white, or clear. Unless of course it is a rare yellow diamond. But you will most likely be looking at a white diamond and you don't want it to have any yellowing in it.
Cut - A well cut diamond refracts the light and gives the stone "fire". It will shine, sparkle and look unbelievable if cut right. If cut wrong, the stone may look dull.
Clarity - A good diamond will not have any visible flaws or clouding. Most diamonds will have some flaws unless they are small because it is very hard (and very expensive) to get a perfectly flawless stone, although they do sell them. You should not have to ask to see the stone under the microscope and you should definitely do this.
Carat - This is the one most people get hung up on, although I told my husband I'd rather have a good stone that was smaller than a crappy one that was big. Carat is obviously the size. Depending on the specs of the diamond, you can get a 1/4 carat for as much as a 1 carat.
Have you considered a different stone? I know diamond is traditional but some women like colored stones.
As far as the color of the band, silver or gold, if you decide to go silver spend the extra money and get a platinum ring. There are several reasons for this. 1- Platinum is a softer metal and if the ring gets scratched, instead of buffing off metal as they do with gold, they just "remold" the metal. You never lose metal. 2- White gold is something someone invented. There is really no such thing. It is a combination of gold and a few other metals. Before it is finished, white gold is still very yellow/grey looking. It is dipped in a silver metal called rhodium which makes it shiny and "white". This has to be repeated 1 time a year, maybe more, depending on the users wearing habits.
Shape and setting are all about preference. If your girl is clumsy like me, make sure to get a 6 prong setting in the largest stone of the ring. A 4 prong can easily fall out if knocked around. Also, look at how high the ring sits. Take into consideration her other jewelry. What kinds of stones does she like? Round, square (emerald cut)....what ever she likes you can find.
This website is a great resource, although I don't suggest buying from them because they are EXPENSIVE and finding yourself a small, privately owned shop will probably be a better experience for you. But check it out and do your homework.
A Diamond is Forever
I definitely agree with watchmakers when he (?) said get some prices first! That way you won't be taken by someone who thinks you have no clue what is going on. Shop around. A lot of smaller, private places will deal with you. You pay cash and they will knock off a certain amount off the price. Stuff like that. Just know what you want and go for it! This should be a fun experience! Not a chore so make it fun! This is a very special moment for both you and her!