Character Tables and Basis Functions: An Opinion Question

This is not a question about how to do a problem. I know how to build a character table and how to find basis functions for a representation.

I am working out of a text written by one of my former Purdue professors. In it he gives an example of the construction of the character table for D3. His approach is to pick basis functions for a representation of the group and calculate the characters. My approach is to calculate the characters using the various theorems, which is simply a Math problem. Then I can decide which basis functions I want to use and can construct the representation from that.

I figure both approaches come out to be about the same amount of work. I was wondering if anyone had an opinion on which approach they liked better (or perhaps one I haven't thought of.) Thanks!

-Dan