Moving from Windows Mail for Vista to some other email client on Windows 7 Professional

Hi there, got a new laptop with Windows 7 Professional.  Tried to migrate my emails from old Laptop from Windows Mail running on Vista to my new laptop and utterly failed.  My email storage folder is quite complex and is about 20Gb in total and I do have several email accounts currently in Windows Mail.  How do I migrate all of my current emails and email structure to the new laptop whilst keeping the current folder structure in tact and without messing up my folders and emails.  I do not care about what email client I need to use on my new laptop.  Could be Outlook or some other ... whatever works best is fine by me.  Help please.  Thanks, Torsten.