Well you are more likely tro get shards from blue items. The different lvls of the items will determine which shard you get. (ie lvl 60 blues are large brilliant shards, but blues from say, SM will only be like small brilliant or radiant, glimmering etc)
For reference the "Green lens of XX" that engineers cna make will always disenchant into a Large Radiant shard.
The greens have a slight chance for a shard but they mostly give Dust and sometimes give essence
For Illusion dust (highest lvl dust) you want greens of lvl 50+ And go down in lvls for each type, ie Vision, Dream, Strange Dust. Strange dust is greens like lvl 0-15 or so.
Basically if you want shards, farm the appropriate lvl instance for the blue DOP drops from bosses. If you want greens then do the same, look for chests and stuff since they drop greens a lot. I.e. msot success will be in instances. Another trick for the lowbie enchanting is pickup tailoring and disenchant everything you make, that will give you a TON of strange dust, some essences and the occasional shard.