Congratulations on the new computer.
To answer your questions, check your programs to see what version of Java you are currently running. Version 7 Update 5 is the latest version. Remove any outdated versions of Java before installing a new version. You will find the latest version here: Java Download
Follow the prompts. Make sure you uncheck any free toolbars or other offers that you don't want, if they are checked by default.
If you are going to install Microsoft Security Essentials, you will need to uninstall Norton prior to that. I would remove it via your Control Panel. Just to be sure, follow with the Norton Removal Tool
that applies to your specific version. Malwarebytes Anti-malware should be no problem installing.
Considering that your Gateway is under warranty, it might be good to post on a dedicated Gateway forum if you have additional questions in the future. There is one HERE
The folks there will be familiar with your model and should be able to help you.
Good luck and enjoy that new computer.