To me, this is a very easy answer, I would go with the
Ipod Mini. Here's why:
Regular Ipod: The new Ipod is expensive, and has a bunch of new tricks, such as video. While video sounds good, this is still in the early stages, and they are going to be so much better in the later versions. Personally, I got one less then 2 years ago. The screen is black and white, and the all it does is music. Eight months later a coloured screen Ipod came out that can hold pictures. Then last month the video ipod came out. I want to throw mine out and get the new one. Your 10 year old would probably be the same way. If it isn't necessary I wouldn't go with the regular Ipod.
Ipod Nano: My DH has one, and they really are nice. Also, for the "cool factor" this might be the best idea. Here are my problems however. The lawsuit diskids2 mentioned is actually about how easy they scratch, both the body and the screen. My DH takes very good care of his, and still has a few dings. I would only think a 10 year old would be much worse. Also, it is the size of a pack of gum. Cool yes, but damn it is easy to loose! Again, fears of a $250 player going through the wash, or being left behind would worry me.
Ipod Shuffle: I see no need. It has no display. It is not the best in any category. I know I am not a 10 year old so I don't know what is cool, but so many other brands have better little players for the same price.
Ipod Mini The mini, while discontinued, is still a great little player. It has a good size harddrive without left over space. The size is small, but not so small that you will loose it easily. The price is okay, and it is the strongest case, which has proven to last through the "drop test". Becuase it was just discontinued, the price is falling. A lot of people are grabbing them up. You are paying the same price for a device that holds more songs. Other pro: cool coloured cases, other con: black and white screen, which might not be so "cool."
I hate to say it, but new Ipods come out every year. I bet when your 10 year old becuase a 15 year old, no matter what you choose, he or she will want the newest one. (I know even as an adult I am the same way

) So I would invest in one that would last until then, and not cost too much.