Best way to upgrade kernel in Ubuntu Desktop 14.04.3 LTS
Solution 1:
Installing from Ubuntu repositories is preferred.
This will install a supported Ubuntu kernel and it will get updates.
If you install a mainline kernel, you may have issues with some drivers, and you will have to update it manually.
Ubuntu kernel 4.2 will be default in the next "point" LTS release 14.04.4 that is scheduled to be out in Feb 2016.
There should be no problems in upgrading to 16.04.
Installing linux-generic-lts-wily
now you install that kernel a bit earlier than it will be released for all LTS new installs.
You can read more about HWE Stack.