Hello,
Given the size of the files & DB, along with the very large version difference the best way (in my opinion of course) would be to copy the site to a development server, and start the upgrade process there.
After it's completed and tested working we could then move it to the live server so there would be very little downtime.
If you have any questions, please feel free to ask.
Thanks!
Keith
P.S. On weekends I only check my message periodically, I apologize for any delays in response.