We've talked about how to build your character with skills, we've talked about what we will face as enemies.
It's time to talk about gear.
It's a huge topic so expect several posts on affixes, a post on socketing, a post on consumables and maybe more.
Gear in Diablo 3 is broken down into types in several ways. Each place on the paper doll has its own gear. Gear for the head slot for example cannot be equipped in any other slots. The exception is rings - rings can be placed in either slot (although not anywhere except those two slots). You may also wish to develop your Followers. Followers have a limited paper doll. You could develop all three followers so that you can choose which one to take with you depending on the situation. Followers only work when you are soloing.
So here's an inventory of the total amount of slots you may wish to develop:
Character paper doll: Boots, Bracers, Gloves, Pants, Shoulders, Belt, Chest, Helm, Amulet, 2 Rings. Main Hand Slot, Offhand Slot = 13 item slots
Gem sockets: up to 14 gems may be socketed into the character's gear
Each Follower: Main hand, offhand, 2 rings, amulet, special = 6 item slots with up to 7 gem sockets.
In total to equip your character and each follower takes 31 items and up to 35 gems.
That's a lot of stuff!
Probably the most important slot is your weapon. Most abilities work off weapon dps. Contrary to what a number of commenters have said it's not weapon DAMAGE, ie the damage range, it's weapon DPS you should look at. This is explained in detail on the Armada theorycrafting forums so I'd like to thank them for their excellent work.
Mods that add to your weapon dps will directly increase the damage of your abilities. All damage in the game is calculated from that number so it's very important. As a general rule get dps up high and worry about other modifiers later.
Gear has a number of properties that are generated from a pool of affixes. The word affix literally means something stuck on something so un- is a prefix (a type of affix) stuck on the word usual to mean not usual. So an item in Diablo 3 with two affixes might be a King's Battle Axe of Wounding. King's is one affix (a prefix) and of Wounding is another (a suffix). Blue items have 1-2 affixes and cannot have 2 prefixes or 2 suffixes. Rare items have 2-6 affixes. Blues and Rares get affixes from the pool described here on D3Inferno. Legendaries (including set items) will likely have unusual preset abilities that aren't in the regular affix pools. (For example in Diablo 2 some uniques and set items had the mod Cannot Be Frozen which was very handy as being frozen slowed down attack speed and movement speed and nerfed you a lot). We don't know these qualities yet as these items are still being worked on but D3Inferno has datamined the affix pool for legendary items.
Most items in Diablo 3 have most of their powers generated at random. So a pair of boots may have +5-10% run speed and 3 random properties. These random affixes are generated from a list that is determined for each item by where it is worn on the paper doll and what item level it is. Item level roughly corresponds to monster level so if you kill a level 30 monster it will drop an item that will around 30 as its item level. Think of this as a top end cap.
Suppose an affix comes in 4 strengths:
Level 9 +5-10% fire resist
Level 19 +15-20% fire resist
Level 39 +20-25% fire resist
Level 59 +30-40 fire resist.
An item can have any of those affixes as long as it is high enough. So our level 30 item at best could have 20 fire resistance. However it could roll the crappy affix and roll badly and only have 5% fire resistance. Even a level 62 or higher item could roll the 5-10% fire resistance property. That would clearly be a very disappointing roll.
So to find an item with the perfect result we need an item of level 59 or higher, plus we need it to get the top one of four different affix types that do fire resistance plus we need it to roll 40 on the 30-40% range. We would also need it to pick the property we most want out of a long list of affixes, some of which are junk for our purposes.
A perfect rare would need to have achieved this improbable sequence of luck 6 times in a row (and of course it would have needed to roll 6 on the 3-6 properties).
Effectively this means you will never have a perfect item, you won't even get an A+ item, the best you can hope for realistically is B+
Here's an example of what a good end game weapon might look like
Exalted Grand Sagaris
Enhanced weapon damage - +48% enhanced damage (from Damage VII). Possibly the most important weapon stat.
Increased attack speed +24% attacks per second (from Haste X). Very important affix.
Max damage +87 good mod but a low value
Improved crit damage +27% (from Crit_D2) strong affix although this is on the low end of the scale
Stun resistance - +10% not a very good affix for a weapon
Sockets - 1 a junk mod, because we could socket it at the Jeweler for gold. This just wastes an affix slot.
Let's compare this realistic weapon with a perfect weapon made by choosing affixes and values.
Exalted Grand Sagaris
Enhanced weapon damage - +50% enhanced damage (from Damage VII). Possibly the most important weapon stat.
Increased attack speed +25% attacks per second (from Haste X). Very important affix.
Attacks per second bonus +0.25
Minimum damage +286
Maximum damage +381
Damage bonus vs Elites +26%
See how the perfect one is much better than the realistic one? So Diablo3's end game will often be a matter of farming over and over in the hope of getting slightly closer to an unreachable perfection.
I've seen a few posters on Diablo 3 boards asking how long it will take to get Best In Slot. There is no hope of ever getting best in slot with an item. It's possible with a gem but a rank 14 gem will be very very expensive.