The video DaddyG pointed to describes the process I use for testing or for migration. There are two things it did not cover; Contacts and Rules.
You said you already have Contacts exported to a .csv file. Contacts in weMail are stored in a separate folder in the same location as the message files
You can follow the same procedure in the video for this folder (rename the new installation folder to Live-empty)
Then copy both the Windows Live and the Live folders to the new system.
If you have any Rules set up, you'll have to edit the registry and export the following key for each User Profile (people who log in to the computer)
HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows Live Mail\Rules\Mail
A quick way to look at the key is to run reg query in a command prompt (std is fine - it's the current user's key)
reg query "HKCU\SOFTWARE\Microsoft\Windows Live Mail\Rules\Mail" /s
Then use the exported reg file to import the rules to the new machine's registry.
Those are the two things not covered in the video : Contacts in the Live folder and Rules in the registry.
Piece of cake!