LE uses the term “unique” for those items, and they are more akin to uniques from path of exile than legendaries from D3. most of them are primarily useful for leveling and don’t have much place in endgame builds, but there are a few that are exceptions to this and enable or enhance certain playstyles. (the prime example of this is the chest armor Exsanguinous, which is a low level item–23 if i’m not mistaken–but enables a low-life, high-ward playstyle.)
we will get legendaries at some point in the future, but it’s not clear what they’ll be like yet.
for loot filters, i recommend checking out Heavy’s basic loot filters for each class. they are a great starting point for customizing your own filter to prioritize certain affixes, and they’re also good to use just to filter out some of the clutter. he also made a guide explaining how to set up the filter on your own.
“shattering” refers to using a Rune of Shattering in the Forge to destroy an item and give you affix shards based on the affixes on the item. each tier of an affix gives you a chance at a shard of that type, which you can then use to craft other items. crafted rare items tend to be the majority of the gear for endgame builds in LE, so it’s worth investing some time into learning the crafting mechanics. the game guide (press G in game by default) has a basic explanation of it, and of course i and other players are happy to answer questions you have here, in the chat in game, or on the discord server. 
the loot hunt in LE is often about finding blue (magic) items with 1 or 2 desired affixes, and then crafting the rest of the affixes to create the item you want. it’s very rare to find a rare item with all the affixes you want. some affix shards are very rare, especially the class-specific ones that only appear on chest and head pieces. many of the rare affixes become more common at higher levels. i always keep an eye out for items with these and other less-common affixes, so i can shatter them and use the shards on gear later.