A blue ceiling is the gateway drug to bold decorating decisions. It's going to feel crazy at first, and then you'll shake your head 4 years later when your daughter looks up and says "Oh my gosh, our ceiling is blue".

3 good reasons to do it, and 1 questionable reason:

Without calling attention to itself, it gives the room an airy feel. Really- people don't even notice it. They only feel it, and it feels fancy in a way you can't put your finger on!
Blue is a receding color - so it will give the ceiling plane an automatic lift.
It really goes with any color scheme. White/ Light furniture and finishes with a blue ceiling? Heaven! Oranges, yellows and reds will look even more orange, yellow, or red. Pair your blue ceiling with green rugs and yellowish curtains and you are outside!
I've also heard that the color repels bugs, and I've heard that it repels evil spirits. I don't know about evil spirits, but there are currently 3 spiders smeared across my blue ceiling, and a giant fly is about to meet the same fate, which brings me to ceiling finish...

Usually the answer is matte. BUT- If you live a life that requires you to occasionally wipe stuff off your ceiling (like you have a 5 year old with a good arm or a lot of spiders), the answer is eggshell. It's wipeable, but not too shiny. It's going to show more imperfections, and your contractor isn't going to like it - but it's your blue ceiling, and it's your right to be a little bit crazy.