I don't see anyone actually addressing why you'd choose to install from repositories vs. downloading from the official site, so...
Command line/Software Center
- note that these are functionally the same (in the background, Software Center will run the same commands you'd run if you installed it through bash). The only difference is whether you navigate the GUI or use command line. I would recommend learning to use command line: It makes things easier in the long run.
+You'll get automatic updates: Whenever you update Ubuntu (whether automatically through software updater, or by manually running
sudo apt update and
sudo apt upgrade), LibreOffice is updated to the newest version in the repositories (this, incidentally, is the main reason to use the package manager: you don't have to worry about whether you've updated program x or y; it just happens automatically, and since it's all from the repositories, you know you'll get a version that's compatible with your system.)
+You'll get a known stable version: There are very unlikely to be any major bugs that render the software unusable
-You'll get a known stable version: It won't contain all the newest bugfixes and features
The official website
+You'll get the latest version, directly from the source. This includes all the latest bugfixes, as well as any bells and whistles you never knew you needed(well, you likely still don't know that you need them, or care that they exist, but hey)
-The version you get may include major bugs: This is not likely for major software like LibreOffice, but finding and fixing bugs is not an exact science.
-To update, you'll have to redo the installation process: Go to the website, download the latest .apt package, and install.
- This is the option you didn't mention. Ubuntu includes a way of adding third-party repositories to the system, allowing you to install software not included in the official repositories via apt. Some software even has official (or officially endorsed) PPAs like Wine and Pale Moon.
+You'll get the very latest version and the convenience of automatic updates
-You have to manually add the repository (thankfully, most PPAs come with explicit instructions on what to do)
-(in case there isn't any official PPA direct from the developers) You'll have to trust yet another third party with the keys to your system: they just might decide to slip by an "update" that actually includes malware. This may be acceptable risk in some cases (indeed, I'm sure many of them are perfectly fine), but I would advice against making a habit out of it.
So which should you use? In case of LibreOffice, you're probably not missing out anything major by not having the very latest version, so I would advice just installing via apt (or Software Center). In the rare cases where you really want to have the latest version (Wine is one example, if you plan to do lots of gaming), use the official PPA if available, or install manually if not. I would, as a rule, stay away from PPAs that don't come directly from the developers, but sometimes you may have to make a judgement call about whether a third party can be trusted.