For those disappointed by the "choose one" problem, a list of items that look the same:
Underworld Helm:
Expert Goldminer's Helmet, dropped by Digmaster Shovelphlange in Uldaman (outside the instance) looks the same, and is usable by any leather-, mail-, or plate-wearing class. For clothies, Miner's Hat of the Deep is similar, but gray instead of yellow, and is dropped by troggs outside the Uldaman instance (in the same location as the Digmaster). There are also several Engineering-specific options that look the same or similar. Complete listing here.
Shatterstone Pick:
Perhaps unsurprisingly, this looks identical to most other mining pick items in the game. Complete listing here.
If you're going for the easiest one to get, and the one usable by any class, you want Mining Pick, available wherever trade goods or mining goods are sold.
It should be noted that Cold Iron Pick, Miner's Revenge, Tunnel Pick, and Rock Chipper are all two-handed weapons and cannot be equipped at the same time as the Deep Core Lantern.
The most "prestigious" and/or hardest to obtain of the look-alike items is probably the Digmaster 5000, an extraordinarily rare zone drop in Uldaman.
Marcus' Pickaxe is available only to worgen and is a reward from the worgen starting zone.
Ryedol's Lucky Pick is a zone drop in the Badlands. It is the only "Unique" pick (Shovelphlange's Mining Axe is Unique-Equipped).
Brann's Trusty Pick is a reward from a quest in Silithus that begins with Brann Bronzebeard's Lost Letter.
Deep Core Lantern:
There is only one look-alike item in the game for the Deep Core Lantern. It is the Everglow Lantern, which was formerly a quest reward from Supplies to Auberdine (Alliance) or Weapons of Choice (Horde). Neither quest is presently available in-game, and so the Everglow Lantern is no longer obtainable. Thus, it is most advisable to select the Deep Core Lantern as your quest reward if you hope to obtain this set look in its entirety.
TL;DR:
Both the Underworld Helm and the Shatterstone Pick have look-alike items that can be obtained in order to match the look of the full set. The Deep Core Lantern does not. Therefore, to obtain the entire "set" look of this quest's rewards, you should choose the Deep Core Lantern.
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