All the World's a Stage
This article is designed to illustrate the basics of roleplaying a draenei, important issues to consider, and links to other articles with relevant information.
Quick Historical Outline
The draenei have largely spent their lives on the run from demons. Under the guiding hand of the Prophet Velen and with the help of the naaru, they fled the demonically corrupted eredar on their home planet of Argus. After settling on Draenor, they began a reserved relationship of respect with the native orcs. The planet was discovered by the Burning Legion, and the orcs were corrupted and pitted against the draenei. Many draenei were mutated into Broken or Lost Ones, but some managed to escape once again with the Prophet Velen. Their craft, the Exodar, had been sabotaged by blood elves, and crash-landed on Azuremyst Isles, in Azeroth.
Things to consider
The important point to bear in mind is that the draenei do not work with the demons. If you decide to roleplay a draenei with the Burning Legion you would need to keep in mind that your fellow Draenei will likely hate you. The Broken and Lost ones are corrupted Draenei, but of course this does not mean they are all evil, but have the possibility to be as such. The draenei would have extreme distrust towards anyone who is even close to being on a demons side so keep that in mind when your character is around warlocks and their pets.
The vast majority of Draenei, as a basis, worship the light. They do not age most likely because of their relationship to the light itself. They are not invincible, but they do not die from old age, either. Counting age by years like other races do probably means very little to them. Instead, they might judge maturity by the actions and deeds done by the individual, or what rights of passage they have performed.
Also, they have a Russian accent.
NOTE: The race itself as a whole worships the light and the Naruu, no matter what "class" the character is.
Priest and Paladin: Draenei by default worship the light and those that take up being priests or Paladins are those who would be able to teach and lead in the use of the light.
Death Knight: All Death Knights have lost the ability to use the light. A Death Knight Draenei is someone who has been completely removed from his or her connection to the light.
VELEN PERSONALITY Wise and not power hungry. Very honorable. Looked up to by many. Somebody people want in real life!
ARCHIMONDE PERSONALITY I know there are people out there who want to roleplay an evil draenei. This guy is cruel and heartless! Will do anything to gain power! I recommend a Death Knight or a Shadow Priest for this class!
Roleplaying ideas and class choices
NOTE: These are merely ideas, and none are obligatory. Do not feel that you have to conform to one of these archetypes. Feel free to create your own!
Army leader: The draenei have entered war and need organized military. Perfect guild oppurtunity there! Classes recommended: Paladin and warrior.
Repair man: The exodar needs repairs doesn't it? Anything that can use a one-handed mace can do this so I won't put recommended classes! I know there's a mace that looks like a hammer if that interests you!
Explorer: The draenei are on a new world so why not explore it? Any class that can take a beating will be good at this! I'd prefer a Rogue and Warrior for this. You could also get a few people to help you!
Medic: As witnessed among the injuries from the Exodar crash, medics are helpful amongst the draenei. Any healing class is applicable to this role, such as priest, paladin or shaman. Consider supplementing with first aid.
Missionary: As the draenei spend a lot of time worshiping the light and exulting in the naaru, some may take it upon themselves to spread the word. Classes with a background in the Holy Light, such as priests and paladins, may be most applicable.
Soldier: While the draenei are primarily a peaceful race, they may need physical prowess to withstand attacks from their foe. Martial classes, such as the warrior and paladin, may be best suitable.
Exorcist: Being a race so interested in upholding the light, there may be some who wish to spend their time and effort deliberately hunting demons and expunging them from places where they do not belong. This may be most suitable for holy classes, such as priests and paladins. In addition, you could try out being a Draenei Death Knight killing demons and Scourge in an attempt to redeem themselves to the Light, or maybe just prove themselves to be a real person and not a mere demon to their fellows. You could try to accomplish this by slaying demons and dark creatures. The Anti-Hero would work quite well with this combo.
Scholar: Magic is something which can be researched and developed over time, and those who dedicate themselves to researching magic and unraveling further secrets may be among the first to make new discoveries. Classes with an intellectual or studious disposition may be most interested in this role, such as mages, priests, paladins and shaman.
Trapper: Draenei require nourishment, like all races, and it stands to reason that their tradition of hunting on Draenor would continue on Azeroth. Recommended classes include hunter and warrior, especially if supplemented with a high level of fishing or cooking.
Self-Standing: This personality involves being grateful for the Narru, but realizing that they really cannot do much without them. They also know that there will come a time when they no longer need to constantly flee and fight for survival. Has a result, they look to make themselves more then just servants to the light, though they still hold it in high regard. A Draenei of this type may find themselves approaching Shamanism has a way to seek out a real identity for their people. After all, nothing is more permanent then nature. They may also work to make the world a safer place through the ways of the Paladin or Warrior so their children can one day lead a peaceful life and be spared their hardships. Death Knights would work for this as well, perhaps feeling empty without access to the light, they seek to ensure even Draenei like them and the Broken can find a place in the world without relying entirely on the light.
NOTE: Please feel free to add any more good ideas to this list.