Kindle Fire Utilties is by far the most easy rooting i have done.
first you run 'install_drivers.bat' on your PC, and wait for it to say it was done. then plug your Fire into your PCs USB port. it should detect and install and then say 'successful' at the bottom. now you can launch 'run.bat' and it will open a command prompt with a few menu selections, there's a ADB STATUS: ONLINE message if it detected properly. now, use the option 'permenant root with superuser' and wait for it to complete. keep in mind there will be tons of sound effects of hardware connecting/disconnecting and you *may* get errors saying your hardware is installed wrong--ignore that!. the Fire will also reboot and do all sorts of stuff. this is normal. when done it will say 'root complete with great power comes great responsibility' or something to that effect. now, go back to main menu. if the adb status shows offline, likely if your Fire rebooted after, wait for it to go to its lock screen and then hit '0' on your number pad and hit enter. it should refresh and show online again. now, select option to install 'fire fire fire'. when that completes, select the option to install optional packages (play store, etc) and when that is done, exit and unplug your Fire from your PC. on first use it should ask if you want default Kindle Launcher or Go Launcher. i highly recommend Go Launcher and select as default as apps like Play store will not work in the default Kindle Launcher. don't worry about your books or anything, the Kindle Launcher will still be available to you in Go Launcher, but it will load as an app. do NOT use 'Kindle' app itself. it will freeze your tablet. use the launcher. and as for the widgets with download links, they will for some reason say 'your device is not compatible' but you can still sideload them on there, i got Go Weather EX and Go Power to work by sideloading the APK and not going through the play store