I've found it particularly straight-forward to get ascended pieces in all slots. All slots except the back.
AccessoriesLaurels or Guild Commendations
Rings Laurel Merchant or BUY-4373
Amulet Laurel Merchant
There appear to be many different options for back pieces, however, their acquisition methods seems to be varied, with some taking more effort than others.
If my primary interest is to get an Ascended back piece, what is the easiest option?