The first two choices on my first chase I wasn't worried about, which was Chiyo (the normal one) and Ino. I had both of them already, so I just went with Chiyo because it gave more fragments (5 versus Ino giving only 3).

My next chase mission gave Tenten and Naruto, with Tenten being 3 fragments and Naruto 5 fragments. I was trying to get Naruto to 3 stars, but I was short from the elite instances (only needed 1 more fragment to reach 3 stars), so I'm glad Naruto was on there so I could upgrade him.

My last chase mission gave another Chiyo (this time only 3 fragments), and a Kimimaro (5 fragments). The items accompanying all of them seem to have just been food.