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.
Best Answer
Treasure parcels are shared among the whole group, not one per character.
This is the Treasure Parcel for Party Level 1, found on DMG page 126:
This has ten treasure parcels, and with a four-person party, you ignore parcel #3 (as you've discovered). Over the course of level 1, you should drop each of these once (except parcel #3).
Parcels 1 to 4 are magic items. Parcels 5 to 10 cover currency, potions and valuables. Each of those lists options of what to drop, and you only drop one of those options for each parcel. The first option is the pure gold option, whilst the other options involve substituting a portion of that gold for potions and/or valuables worth the same amount as that portion of gold.
So for parcel 5, your party would receive either 200gp, or two 100gp gems, or two potions of healing (worth 50gp each) + 100gp. They would not receive all of that. No matter what they get, though, parcel 5 gives them 200gp worth of stuff.
No matter what option you pick for each parcel, since they work on an equivalent-exchange basis, your party will end up with 720gp worth of stuff by the end of level 1 (on top of their magic items). This is the "Total Monetary Treasure" value referred to in the top right.
So at the end of the level, your party might have:
... as well as the level 2, 4 and 5 magic items.