That is an eternity for that little data. You should install and patch Oracle to the correct release on the new server, create a new database with all of the table spaces that you need, the correct SGA size, setup RMAN backups on the new database, create all of the users that you need with the correct privileges. And then use data pump to get a full export of the schemas that you need and import that into the new database. If you want it to be really fast and you have enterprise Oracle you can add compress=all and parallel=5 to shrink the export size and make it uber fast. Like instead of taking 20 minutes to migrate your data you might be able to migrate you data in 5 minutes. Do a few test migrations, test the Linux version of the database and schedule you migration. You should need less than 2 hours of downtime.