Any kind of blond or brunette shade would probably work well. In order to pick a good shade, you're going to need to consider whether warm or cool colors look best on you (as a general rule, if silver jewelry seems to "match" your skin tone, you should go with cool colors, and likewise for gold/warm) and choose accordingly - most hair colors come in "cool" "neutral" and "warm" tones.
Personally, I like darker hair with pale skin and blue eyes, but you really do have to be moderate with how dark you go - as the other girl here said, go too dark and you will look even paler and totally washed out. You can compensate for that with lots of mascara, eyeliner, and blush to make your features pop again, but if you'd rather not change your makeup routine almost entirely (assuming you wear something different right now), stick with shades that are within a level or two of the color of your eyebrows. I'm naturally blond with pale pinkish skin and blue eyes, and I've dyed my hair multiple times to a medium cool (ash) brown and loved it. Spend some time looking through hair colors, take a friend to tell you yay or nay, and pick something you like!
definitely keep it on the lighter side. Blondes, dirty blondes, and light browns will all be flattering. Guys typically say "dark brown or black" for these questions because they like the idea of the contrast between dark hair, pale skin, and light eyes, but honestly that's the WORST thing you can do. It'll wash you out and look awful if it's not natural (trust me I've done it). Don't stray too far from your natural color as those shades tend to look best.
it depends on the person really. I like her hair. it depends on your natural hair. with light skin and eyes you can pull off light hair better, IF your natural hair is light brown or lighter and you were a blond child.
but, if you have naturally medium brown or darker hair that is true brunette you probably would look fake as a blonde.
it is good to stay in your own family. like if you are a redhead stay some shade of red. if you have medium brown hair you can go a little darker or lighter but I wouldn't advise going blond. if you have deep brown hair I would not lighten it up too much, definitely stick in the brown family. if you have hair that is some shade of dark blond or very light brown you can go blond but not too light. etc.
i think those are good guidelines.
example I have light eyes and light skin and my hair was blond as a kid, now it is some mix of dirty blond and light brown that it is "blondeish" and much lighter than a brunette but not quite blond, so I want to lighten it or highlight it. a lot of people including hair dressers say I can pull this off fine because my hair is naturally light.