The risk of crashes is highest with release candidate new kernels at this time February 4, 2017 version 4.10 release candidate 4.10-rc6 is the newest. Mainline kernels are considered stable and the latest version here is 4.9.8 which I installed a few hours ago.
Finding the right kernel
Rather than the link you are using, go to (kernel.ubuntu.com - Kernel PPA Mainline) and press the End key:
Now click on the link
4.9.8 and this screen appears:
Note the links with the black airbrush marks. These are the three we will download for Ubuntu 16.04 64-Bit using Intel or AMD processors.
Installing using Terminal
Open a terminal session with ctrl+Alt+T and use:
cd Downloads # Assuming this is your browser download directory
rm *.deb # This erases all *.deb files, ensure only old ones are here
Now toggle back to the download screen above and single-click on all three of the
.deb kernel downloads. After downloads complete (you'll see status in your browser) toggle back to terminal session and use:
sudo dpkg -i *.deb
Voila! - you are running the latest kernel when first option in grub boot menu is selected. Your older kernel versions are still available under grub's Advanced Options menu.
After installing the newest kernel a dozen times you will ask the question "How do I remove older kernel versions?" and you will find those answers here and here in Ask Ubuntu.