I got the update for the new version of the Update Manager 4.7.8 and the Box is ticked to Update, should I update to this?
Yes, otherwise you may not get updates. When I fired up into LM 17 this morning on one computer, it was the first thing shown. Only after I applied the update, then others followed, of which I installed all that applied to me. Note that I don't apply all Level 4 & 5 Updates. In this case, why install a (Level 4) ATI graphic update to a notebook that has only Intel graphics? Nor am I going to install a (Level 5) beta GRUB update. This is the bootloader, no I'd prefer to keep that stable.
Once all updates were finished & I rebooted, this wasn't required, but I do it to ensure that the updates install properly, I then proceeded to upgrade to LM 17.1. Only took 5 minutes or so, click the "Edit" tab of the Update Manager, there will be an option to upgrade to Linux Mint 17.1. It's necessary to click the information links & at least scroll to the bottom of the page, whether or not one cares about the content or not, but I do recommend to read, there will be two of these. One includes that 17.1 will be the one for future upgrades until 2016 arrives, so enjoy a relaxed experience for over a year.
Then the Upgrade can continue, a few updates downloads, and the OS files re-installs itself in front of one's eyes. At the end, there will be a prompt to reboot & it's over. 5-10 minutes total for most users.
Linux Mint 17.1 MATE or Cinnamon successfully updated! Best upgrade installs (I done two computers) I've ever pulled off.
And to think, the first computer that I upgraded to 17.1 was the hard way, creating media on a 2GiB SD card, though it was still a RC at the time. Had no idea it was going to be this painless.
KDE & Xfce users will have to wait it out, still haven't found anything out in regards to these versions. It's likely that any upgrading will have to come from those forks. MATE & Cinnamon are unique to Mint (created by the team), while KDE & Xfce are not, other Ubuntu based distros uses these, and the Mint Team decided long ago, before 17 was released, that they were no longer waiting for Ubuntu to move before they did between LTS releases.
So it could be that Mint KDE & Xfce users may have to wait until the next LTS for an upgrade, though not to worry, updates are continual through April 2019. There will be another LTS release way before then.