As a side note, rman is very fast when backing up to solid state disks. If you can get your hands on some put them in a raid you'll probably back up and restore in probably less than 30 minutes.
In either event, here's how to move the db to another host with hardly any downtime. Here's the overview:
1. do a full rman backup.
2. copy everything in the flash recovery area to the new host
3. go through the process of restoring the db to the new host.
a. There are a handful of steps to do this. It's not too hard.
b. First the full backup is restored.
c. Then each archive log is applied to the new instance.
d. When all of the archive logs are have been applied, the db is opened.
Keep the production db up and running while you are doing steps 1,2,3a,3b. This may take a few hours if you have slow disks/network.
Once the level 0 backup is restored, apply the archive logs sitting in the flash recovery area which you copied in step 2.
At this point, all you need to do put the production db in read only mode and then copy and apply the last set of archive logs which were created after you copied the FRA. This should be very fast.
Then open the db and change clients so they now use the new db.
Best Answer
If you include PLUS ARCHIVELOG in backup command, transactions that happened during the backup will be recorded in a separate file.