Yes,
in a nutshell, TEST!
You don't want to be in the position of having a broken upgrade with no way back. I therefore recommend that you take an image of the server before you do anything, and store it away safely. Test and verify that you can restore this image.
Get a second server, build the latest relevant version of Linux on it, and install Oracle clean from the latest version, either on disc or by download from Oracle. Get the latest Oracle patch set and apply it. Then rebuild your databases on the new server. Test each in turn, and when it's working back it up.
If you really have to do the upgrade route (instead of the clean build), then your upgrade must be completely automatic. Script the whole thing, and when it first fails, fix the problem by altering your script. Restore from your backup and go again, fixing the next problem. Repeat until the upgrade is perfect and automatic. Then one last time, restore from backup, and upgrade, knowing in advance precisely how long this will take and that it will succeed.
Knowing the duration in advance is essential, as it allows you to schedule a long-enough outage to complete the work, when you come to do it in production.
Regards
T