How do I get the iTunes column browser shown by default on Shared device?
If you upgrade to iTunes version 10.7 your problem may be solved... 
In 10.7 you can right- or control click at the top of the column browser (first column) which will show all the options that can be visible by default -- genres, albums, composers, groupings-- in the first column. You can check those that you want. Upon restart those checked options will be visible by default.