First, do burn the restore DVDs and verify they do work. If they don't, give HP a call, explain what you did and why it failed, and they may send a complete set while your machine is still in warranty. But if your first burn works, make a backup copy of your restore DVDs. This ISN'T overkill. Put your restore DVD's in a secure and protected place. It amazes me how I can pull them out 6 months later, and they are blemished without anyone touching them. :).
Next, do get a router to have a hardware firewall between you and the internet. And immediately, if not before you get on the internet, put on virus and malware protection. Microsoft Security Essentials is what I use. If you're happy with what came on the HP, then activate it. But most times, to keep what comes on your machine updated, you have to pay a subscription price. MS Essentials has handled everything that has tried to mess with mine. Malwarebyte is a good one for malware, and is kept updated.
Now it's time to use your HP Advisor, and make sure you are caught up with the updates that HP says you need for your machine. If you're not familiar with drivers, bios updates, version numbers and the like, find a geek that is. For a few mountain dews, get your machine caught up, and note what one's you've done. Not all updates need to be done, necessarily, but if you have to do a restore, you start over again, excepting for firmware and bios updates.
From here it's time to remove bloatware. If you're not going to use it, remove it. Use CCleaner to clean up the remaining traces left behind. Do this before doing Microsoft updates, as you will often get rid of unneccesary updating. Somewhere in here with everything going on, defragging the harddrive is a good idea. Defraggler has done a good job for me. Even after updating from Microsoft, defragging helps your machine run more effeciently and prepares it for the next step.
Now get a program to partiton the harddrive. Partition Wizard works fine. Give yourself enough room to use Microsoft's Backup to backup your c-drive, after doing all of this, on your new partiton. In most cases, if your system gets hosed, you can use Microsoft's Restore to bring your system back to this stage. You can add applications and the like you know you'll ALWAYS use before the backup, and it will be loaded also on a restore. You can give yourself some extra room on the partition for other backups of documents, downloads, etc., but remember, if the harddrive fries, you've lost it all. A good external drive can be used instead of making a partition, but they can be fragile when it comes to life expectancy.
Plan your backup scheduling of your system, and you should be good to go.