I personally use a mix of dubias, BSFL
(aka black soldier fly larve, aka calciworms, aka phoenix worms, aka reptiworms), butterworms, and the occasional silkworm, hornworm and superworm (for 16"+ dragons)
BSFL or
whatever you want to call them, have incredibly
high amounts of calcium, thus letting you feed them directly to your beardie
without dusting them with additional calcium.
They can last up to 2 weeks kept at temperatures approximately around 50-55 degrees F (easily achievable by using wine/beer coolers)
They can get very costly, so it's best to feed them in addition to other insects. (or "breed" them yourself)
Butterworms (aka trevoworms) are another insect
high in calcium, similar to the BSFL, they can be fed directly to your beardie
without the need to dust them with calcium.
Though unlike the BSFL, they can be kept for long periods of time in the refrigerator.
And as with the BSFL, they can get costly, so feed them in addition to other insects.
(They cannot be bred, due to them being irradiated before they are imported to the states.)
Hornworms (aka goliath worms, aka tomato worms) I'm not sure whether or not you'd want to use them as a staple, because they have a high water content, and can cause watery poop, which isn't fun to clean up!
They can be used as a treat, or to re-
hydrate your beardie.
They grow very big, very fast, so they're great for the larger sized beardies. Though they grow as much as you feed them. Feed them little, they grow little. Feed them copious amounts, they'll grow tremendously.
They can last up to 3 weeks at 75* F
If you have LARGE hornworms and don't have anything to feed it to, you can pop those in the fridge and they can last a couple more days.
(can be bred)
Silkworms, similar to the hornworm, grow as much as you feed them. Low in fat, and are relatively high in calcium, they are great soft bodied worms to feed.
They can grow up to 3 inches in length.
They should be kept from 78*-88* F
(can be bred)
Superworms, one of the easiest feeders to get, and can be incredibly cheap.
Though many advise you should wait to feed any beardies superworms until they are
16 inches or longer in length, due to a kink in their digestive tracks that have yet to lengthen out.
They have chitin, which is an exoskeleton unlike the other above mentioned worms, that can make it harder for the beardie to digest, though it is not impossible. They are also relatively high in fat compared to the other worms.
As a tropical species, they cannot be refrigerated, or they will die. Room temp up to 80* F is ideal.
(They are easy to breed, but require lots of time.)
Sources:
http://www.greatlakeshornworm.com/faq
http://www.silkwormshop.com/benefits.html
http://www.phoenixworm.com/servlet/StoreFront
http://www.nyworms.com/butterworms.htm
http://www.nyworms.com/superworms.htm
So in short, best feeder insects IMO are Dubias, BSFL and butterworms.