When you’re playing Diablo III, whether it’s alone or with a friend, there are essentially three different ways you can try to handle combat, and not every character class can use every method.
The first method is melee. This is the specialty of the Barbarian and Monk classes, and in a pinch the Demon Hunter or Wizard can almost sort of hack it. When you’re setting yourself up for melee-range combat, you want to have your Primary and Secondary skills function best at short range- probably with an area, since monsters like to swarm. Invest heavily in defensive skills as well, and make sure that your gear has at least some +Vitality and +Strength for the increased Life and Armor that you’re going to need. As gems go, while Dexterity for Monks and Strength for Barbarians are obvious, sticking an Amethyst in your helmet for increased Life rather than elsewhere for increased Vitality is an important option, as is the off-hand item- Shields are usually the way to go here unless you find a particularly tempting other off-hand option. Monks and Barbarians can go without shields for melee (and usually want to, so they can get a much bigger hike in damage output).
The second combat method is mixed. The Barbarian and Monk can kind of do this, but it works best with the Wizard or Demon Hunter. Both these classes have a mixture of short and long range skills that will let them be a constant source of damage for their enemies. While a Demon Hunter or Monk is going to want to focus on their mobility for mixed combat, as both have not only an array of mobility skills but a lot of interesting support capabilities and plenty of resources (spirit/hatred/discipline) to call on, the Barbarian and Wizard take a more stoic approach- stand there and beat on things as they approach, changing skills as necessary/appropriate. Demon Hunters and Monks are naturally going to focus on Dexterity for this- not only does it boost dodging, they’re both Dexterity classes to begin with. Barbarians will want to invest skill and rune choices in things that bring enemies nearer, strike at a distance, or cause strange support effects to happen (Call of the Ancients anybody?). They’ll also want to put a lot into their Intelligence since they’ll take a lot of hits from spellcasters. Wizards will want to invest in their magic Armors heavily, and bolster that with Vitality and Health increasing gear and gem choices. Frost specialization is a good option for them also, allowing them to increasingly debilitate enemies the longer the fight lasts and the closer the foes get.
Long range combat is your third method, and the Monk and Barbarian really aren’t capable of this. You can sort of kludge things together, but both of them will quickly run out of their resource and find themselves unable to really regain it well enough to function. Demon Hunters, Witch Doctors and Wizards, however, function very well at this range, almost by default- only the Wizard really has trouble and only in their Primary skill choice, since a lot of those options haven’t got a lot of range. Ranged combatants will want to invest in their main stat first, but also have a decent amount of Intelligence on the side for Demon Hunters and Dexterity for Wizards and Witch Doctors. Most of what’s going to come at you will try to reach melee, too, so skills that knock things away, pin them in place, or distract them with something other than you are premium options here. Runes for slow, freeze, knockback, or stun are also your friend.