Mods

"What are the best mods out there" is really subjective and not a question that someone else can really answer for you. It all depends on what kind of mods you like. If you're into mods that only tweak small portions of the game, you probably won't like the mods that overhaul the game adding hundreds of new blocks and items, and vice-versa. If you want to know the most popular mods, CurseForge is a good place to look, as most modders use CurseForge to host their mods.

As far as downloading .jar files, you download them like any other file. If you're looking to install Forge (the main mod loader that modders use) and start using mods, here's a video that shows how to install Forge.