Power is relative, but in general the “order” would be:
Normal (White)
Blue (Magic)
Yellow (Rare)
Purple (Exalted)
Set (Green) and Unique (Brown/Orange) are “on the same level” if that makes sense.
For this list Weaver’s Will Items will count towards Unique items.
Legendaries are Unique Items that have additional added stats to them (Either on a regular Unique or on a Weaver’s Will Item). So there are no Items that only exist as legendary, all Unique Items can be legendaries. (With a few exceptions from story rewards)
Legendaries would be “the most powerful” item rarity across all items, with some caveats. Just because they have a lot of extra stats doesn’t necessarily makes them super strong, there are also a lot of “bad” legendaries. And there are some things that are mututally exclusive with Legendaries, namely Set Affixes and Champion Affixes. These only can exist on Magic, Rare or Exalted Items
“better” is a bad word to use here, because it depends on what the Base Unique Item is and what legendary stats it has.
A very good exalted item on a good base, with good exalted affixes can be equally powerful as a legendary item. For legendary items it always matters how many legendary stats it has (It can have 1-4 legendary stats on top of the regular Unique).
But in general the top end for a Legendary can be a lot higher than an exalted item.
It is really build dependend, there are a lot of builds that can utilize a lot of Uniques and thus also can have a lot of Legendaries.
For the very top end, many builds can use uniques with high legendary potential and put some legendary stats on them just to get more stat budget than a regular exalted item.
So the higher you push a character, naturally you will have more Legendaries.
That is the usualy case for the vast majority of buidls that you will play. Having a mixture of Exalted Items and Legendaries. Depending on your build you might have 2-3 Set Items (Either Set Items directly or Set Affixes crafted onto an Exalted/Rare Item and maybe one Champion Affix Item (either rare or exalted).
When a unique drops it will have 0-4 Legendary Potential. Depending on how much it has you can do multiple things with it:
- if it has 1-4 LP craft it together with a 4 non-sealed affix exalted item to get 1-4 Affixes added to the unqiue
- If it has 0 LP put it into the Egg of the Forgotten Knight in the Nemesis Rewards Screen
- If it has 1-3 LP use the Farsight Turtle Woven Echo and try to increase the Lp by one
Most shards become worthless at a certain point, but depending on how much you craft rares and exalted items you always want to have some shards. There are some particularly rare shards however that are always worth shattering/rune of removal to get many of them, because they are very rare and hard to get, like Hybrid Health and Class Specific Prefixes.
I also highyl suggest you look into the Ingame Game Guide (press [G] ingame).
It explains all the legendary/uniques crafting and explaisn rarities of items as well.