What can we infer about the girls based on what they want for Christmas?

Well, all of the girls except Beth grumble about being so poor, and Jo even feels that Christmas won't seem very Christmas-y without gifts to exchange. Apparently, Marmee thinks that presents seem like a trivial concern when there is such a terrible war going on and their father is away, serving the troops and in danger. Meg, Jo, and Amy's responses are, at first, somewhat materialistic, and they seem to indicate a certain lack of maturity. 
The girls, at first, decide to buy themselves gifts: Jo wants to buy a book that she's coveted for a long time, Beth will buy new piano music, Amy wants some drawing pencils, and Meg "[thinks] regretfully about all the pretty things she [wants]." These desires tell us a bit about each girl's personality and tastes: Meg is somewhat vain and cares a great deal about her appearance; Jo doesn't care at all about her appearance, only her mind, and she lives to read and write; Beth is the sweet homebody whose desire for herself is actually something that will brighten the household for everyone in it, music; and Amy is rather self-centered, sort of a stereotypical artistic type. The girls aren't evil or mean or selfish to a fault. Rather, they just seem to lack the perspective granted older folks who've witnessed tragedy and felt pain, but the girls do seem to develop perspective quickly as they turn their attention toward treating Marmee and the Hummels generously.