The key facts to remember are to be Human and to choose the Commoner story line. Everything after that doesn't matter much but the find parents quest line is slightly faster if you plan to farm the 2nd key.
Class Choice: I have tried most variants of all classes and learned that ranger and guardian are the quickest for me to get through the story with. I can get a key in ~15-20 minutes. The 2nd key usually takes me an hour and the third key takes me 2 hours. This is why I only farm the first key each week.
Gear: This will only matter to those who bought the special edition of the game. You get a hero's band ring and a golem banker to start with on all new characters, which is perfect for key farming. You get the additional +2 to all stats and the ability to open up your bank to access gear and consumables.
Walkthrough:
To start off with you will be placed in Shaemoor. Do not talk to the green asterisks like you are supposed to. Instead follow the arrows on my map below. Run down the hill, through the watermelon fields, down into the river, and up the hill. If the giant hands haven't spawned then you will need to run across the bridge into the garrison to spawn the champion centaur. Additionally, you can access your bank using your bank golem or using a pass in your shared inventory slot (such as armistice). Get yourself to level 10 using boosts. Then open your map and use the waypoint. This will bypass the entire intro boss fight.
After killing the starter boss, or using the waypoint, you will be placed in a house in Shaemoor. Immediately exit the cut scene and accept your reward. Immediately go north into the city and get to your home instance. You'll want to take the upper route past the queen's throne room and grab that waypoint on your way to the 'Salami district' which is your home instance and will have a green indicator on the map.
Run straight to the bar to talk to your friend and exit the cut scene immediately. Kill all of Big Nosed Ted's henchmen downstairs. Utilize your Stalker pet's F2 skill for 5 stacks of might whenever possible. You will quickly kill everyone with this much might. When you head up stairs following after Ted and Jake, be sure to shoot Ted while he's still yellow. This will skip his little cut scene and also allow him and Jake to damage each other. Once all the bandits are taken care of head down stairs and get your reward. You should then take the power gloves for your reward and equip them.
Your next mission is desperate medicine. Waypoint back out to Queensdale next to the Lieutenant and talk to him. Then run to the farm and pickup some hay on your way to the bandit caves. This helps you get swiftness every few seconds on your way to the caves in case you don't have a mount (hopefully you have a mount). Once in the caves again run straight to the Moa's. Kick the King Moa's butt and watch them run. Wait a couple seconds then follow them as most the bandits in your way should follow them as well. Head straight for the ramp on your right in the next room and go up. You can one shot the few bandit recruits who spawn, then take care of Jake and his body guards. Grab your medicine from the supplies and finish off Jake. Waypoint back to the Lieutenant to tell him your news then waypoint back to your home instance in Divinity's Reach.
Now you will be on the undercover mission. Waypoint back to Shaemoor and run along the cliff's, through the cemetery, and to the bandit hideout. Once in you will have to take down 1 guard and take his clothes. Then enter the hideout. Once inside run straight and drop down next to Johnny. Talk to him first then run across the water and kill the drakes. Take the fuses from the box and go to Blaize. After talking to Blaze you can then kill the final rifle wielding Deadeye Della to end this mission. Head back to Divinity's and go to Logan's office. Once you talk to Logan be sure to take the Orphanage!
Now head back to your home instance and go to the orphanage which is on your right as you enter the mission. If you're struggling at staying alive then do not take down the door. Instead target the 4 bandits directly in front of you inside the orphanage behind the wagon. You can shoot and use AoE through the walls and take them down 1 at a time. Once you kill these 4 bandits then you can take down the door and take out the next group of 4. Remember you can shoot through walls so be sure to take advantage of that to avoid taking any damage. After you kill them you can head upstairs and finish off Ted. Then run out of the orphanage and straight to the hospital on the other side of the instance so you can talk to the Lieutenant as soon as the cut scene pops up. If you're quick enough you don't have to stand around waiting for Serantine to show up.
The final part of the story missions will be heading back to Logan's office. Talk to him and the countess then head downstairs into the far jail cell. Staying alive is "key" here so if you're struggling to stay alive or do damage then simply hide in the jail cell and hit with ranged attacks. The sword illusions will do all the damage you need and Logan will tank. Once finished you'll get your key. You can use your golem banker to deposit your key and gear and be on your way. If you don't have a golem then you will need to press the swords button at the top of your screen and enter the mists to access your bank or utilize a pass such as armistice.
After you have your key you can delete your character or you can farm the next 2 keys, which is another hour each and I don't recommend it personally.