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Just to clarify tings. You have:
An older computer with Windows ME.
A newer computer with Windows XP.
There is a wizard to transfer files and settings from one PC to another. But it will not really do what you want.
As for a Flash drive, not many have enough space for everything. So you would have to do it in stages. However, most application programs cannot just be copied from one PC to another. Programs like games, editors, spreadsheet and database all have to be installed all over again.
Of course there is not problem making copies of your photos, documents and video or other things that bare not programs.