DnD 4e was balanced around the idea that monsters have an AC around level+14, other defenses around level+12, attacks against AC around level+5, against other defenses level+3. There are slight deviations, Solos have more of everything, Soldiers have more defenses, Brutes have more Fort, less Reflex and attack, but these are the approximate numbers.
On the other hand, PCs should have attacks and defenses along the same numbers. They gain attack bonus equal to half their levels, +Attributes, +Expertise, +Proficency (if Weapon attacks) and +Enchantment bonus from the magic items. The same is true for AC and other defenses.
For this reason it is essential that they have the Enchantment bonus they should, otherwise the level appropriate challenge (according to the DMG) will kill them easily. This is not so big a difference in low levels, no magic or +1 is not a big deal, but +6 or +2 could mean life or death at level 27.
This means magic items are not a story element like in earlier editions, but as an integral part of a character as feats for example. So the question is not whether the Dwarf Barbarian should get a magic hand item, but rather why does he not already have a neck slot item, and how high is the bonus of his Weapon and Armor.
Some people, mostly those with roots in DnD 2nd edition, are not comfortable handing out magic items like candy at Halloween, and think magic items are a gift and something special.
If you are one of them, you should consider introducing the inherent bonuses as described in DMG2 and perfected in the Dark Sun setting book. It takes care of the numbers, and you can keep magic items rare and interesting. It is also a good guide to see what kind of bonuses PCs must have from Enchantment.
If you do not have access to any of these books, just remember to upgrade every main item (weapon/implement, armor, neck slot) after level 1, 6, 11, 16, 21, 26. If this is taken care of, you can give other magic items.
From the DMG on page 133 (very bottom of the final paragraph):
Over the course of a typical campaign a party finds treasure hoards amounting to seven rolls on the Challenge 0 - 4 table, eighteen rolls on the Challenge 5 - 10 table, twelve rolls on the Challenge 11 - 16 table, and eight rolls on the challenge 17+ table.
In an earlier paragraph it explains that each treasure hoard should have at least 2 rolls on the appropriate table and that if the hoard seems too small you can roll keep rolling on the table. This makes it so that you as the DM are free to distribute treasure at a pace that makes sense for your campaign. In general the DMG tells us that there should be a treasure hoard when it makes sense in the fiction.
So for example the 7 rolls on the Challenge 0 - 4 table can be divided into two hoards: one hoard found that you populated by rolling twice on the table and another hoard consisting of 5 rolls worth of treasure. Or 2 hoards of 3 and 4 rolls. Or 3 hoards with 2, 3 and another 2 rolls.
It should also be noted that the different challenge tables don't necessarily correlate to the tiers of play. If the party hits level 5 and you haven't hit all seven rolls on the 0 - 4 table don't sweat it. Even at high level the party can still encounter lower CR monsters that would have hoards from the 0 - 4 table.
Best Answer
Analysis of AD&D treasure types.
There are considerably more monsters for AD&D so here is a doc that lists out each monsters.
A is no longer the Man Treasure Type, is not commonly used either being reserved for the Lich, Locathah, Men Bandits, Squid Giant, and Troglodytes
B to F are still pretty much like their OD&D counterpart with the same rough ascending order of value.
G is no longer just for dwarves. Elves are thrown in as well as a bunch of other creatures.
H is still the hoard treasure for Dragons. Interesting the white dragons don't get this treasure type. Along with the Dragons the Archdevil Geryon and the Guardian Naga have this treasure type.
I Interestingly the Roc has been removed from I but more creatures were assigned to this treasure type than OD&D. It also was used a lot with creatures with multiple treasure types, probably because of the Gem and Jewelry values.
Now to the new types
J to N are meant to be assigned to individual monsters. When listed as part of a lair it looks to be incidental treasure. This especially clear for the various varieties of Giant Spiders.
O and P are low value coin treasure types, O is copper and silver, while P is silver and electrum
Q is a used a lot and in conjunction with other treasure types, It is the Gem treasure type.
R treasure type is similar to G but without any magic items.
S is the potion treasure type
T is the Scroll treasure type
U is a high value treasure type with Gems, Jewelry and magic items. The elite monsters that get this are Orcus, Asmodeus, Tiamat the Chromatic Dragon, and interestingly enough Ixitxachitl Guards and Androsphinxs.
V is just magic items
W is similar to G and R but with map instead of magic items. It only used for the Men, Buccaneers.
X is miscellaneous magic items plus a potion, it been assigned to a lot of monster in conjunction with other treasure types.
Y is just gold pieces
Z is similar to H with a smaller number of magic items the monsters that get this are Men Dervishes, Men Nomads, and Will-o-the-wisp. Looks like there is a lot of wealth hidden underneath those camel sacks.