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Use Win7 Professional x64 English Official ISO Download
Write to stick or burn to DVD using tool provided in Step 2 of Clean Reinstall - Factory OEM Windows 7.
F12 Diagnostics should have tested all of your hardware. Did it offer that option? Either way it's up to you if you want to keep that partition since other bootable hardware tests exist, especially if its only offering a HD test. In that case it would be better to delete all partitions to get it cleanest.
As to your backup, its always good to browse in to see that your files are all there. The tutorial Clean Reinstall - Factory OEM Windows 7 provides a checklist of everything that needs to be remembered since it compiles the experiences of thousands of installs including ones where data was accidentally left behind. So double check against the steps.
Keep asking back questions as we will help see that you get it perfect.
Most important is to put your network adapter driver in the backup so if it isn't provided during install you can install it to get online, enable Automatically deliver drivers via Windows Update (Step 3),
then run all rounds of Important and Optional WIndows Update, with reboots, until there are no more when you Check for Updates. You can do these as you set up your desktop and isntall other programs, but since you had problems with your last install I would allow time between each group of Updates and then each program install to see which, if any, is affecting performance.
If you want to try to repair your existing OS you can try a Repair Install but since it reinstalls Windows while keeping everything in-place it might not help if you have corrupt settings or botched the install otherwise, plus it will probably take nearly as long.