How can I update iTunes on a windows 8 asus laptop?

I recently bought an iPhone 6s and I'm trying to restore my backup from my old iPhone. But my iPhone 6s is not compatible with the version of iTunes I currently have, so my laptop prompted me to update it to version 12.6.1. Halfway through the installation, it stops, and a window pops up that says "iTunes has an invalid signature. It will not be installed."
I can't restore the backup until I update iTunes, so I tried to back up my old iPhone to iCloud, but every time I try, a window pops up that either says "there's not enough space to complete the backup" or "the iPhone has been disconnected" (which it hasn't.)
I don't have time to go to Verizon or the Apple Store for the next 3 or 4 days, so I'm out of options. Any suggestions?

Go out and buy a real computer… MAC's use propitiatory applications that make you register your data with a server that then checks to make sure that the items are identical and then gives you the privilege to transfer the data. Where Microsoft just lets you transfer whatever you want from wherever to whatever without annoying programs to update or rules to follow. Oh and you pay 3x as much for the exact same hardware but with one difference is that apple logo… To make you feel all warm and fuzzy

Download and install the latest version of iTunes from the Apple website
https://www.apple.com/.../download/