Piping in with a female perspective (& recently engaged):
1) Go with the surprise. I was so happy I was surprised. It shows you put the time and effort into thinking about this. Note: It doesn't have to be a major production.
2) Ring size: Take one of her rings that you know fits her (if she won't notice) and get the size from any jeweler in your neighborhood, then replace her ring where you got it from. 2nd option: trace the inside of one of her rings (if you can). 3rd option: try to figure out which of your fingers matches her ring finger (left hand). You can do this when you're holding hands, or eyeball your hand next to hers when her hand is flat on her lap, etc. If unsure, just go a size above your best guess -- jewelers can always resize a ring after you buy it. It's easy to do and they won't charge if you bought it from them.
3) Shine counts. I literally look at my ring every day b/c I notice the sparkle. Ignore the guy who said women are all about carat count. Find a balance of carat, color and clarity that you can afford. Make it sparkle. She'll love it. Jewelers can show you how different carats, colors and clarities change the way a diamond looks.
4) Go with a jeweler you get a good feel for. It doesn't matter if it comes from a "name brand store." If you like the people in the store and get a good vibe that they aren't ripping you off - that's the store to go with. You'll probably end up going back there to get your wedding bands anyway, and she can pick out her own then.
Good luck!