This is a pretty fast run that I have been using to get money to buy the ridiculously overpriced A4 gear. It may be pretty obvious how it works but it never hurts to post. It currently takes me between 20 and 25 minutes to complete each run with 0-1 deaths per run (just depends if I get some awful affix and derp out on kiting).
1 - Set your quest to A1Ch4 "Reign of the Black King - The Royal Crypts"
Once you spawn up in Tristram head to the Cemetery of the Forsaken waypoint. Sometimes you luck out and there is a yellow skeleton mob wandering around some part of the graveyard. If he is there kill him and get your first stack otherwise head into one of the 3 open crypts. Proceed to kill everything in the 3 open crypts. One of them is going to have a 2nd floor to go down to but don't bother going down since there isn't anything down there 90% of the time.
Yellow Skeleton in GY
There are 2 events that you are going to encounter with regularity here.
The first is Lady Dunhyld. If you come across her make sure you clear the area around her of Elites/Champions. There will always be 1 near her event sometimes 2. You receive 1600g and a bunch of items for completing this event.
Lady Dunhyld
The second is the Jar of Souls. This one is pretty easy; You simply click on the jar and kill skeletons until the timer runs down. You receive 800g and a few items for completing this event.
Jar of Souls
2 - After you have cleared out all 3 crypts you should have 5 stacks of Neph so head to the Cathedral Garden waypoint. Check for the 2 chests that spawn up here and break/open all the other containers.
3 - Once you have finished checking around the Cathedral head to The Old Ruins waypoint. Head to the weapon rack and then circle around through the town breaking/opening all the containers. If there is a cellar spawned go down and clear it otherwise head out of the northwest entrance to the town and check for one more cellar.
4 - Now that you have cleared out all the easy loot head to the Cathedral Level 3 waypoint and clear your way to the Skeleton King breaking/opening containers on your way. I tend to encounter at least 2 more packs of champions or elites on my way down but sometimes there aren't any. Kill the King and warp back to town, salvage, sell, repair, and repeat.
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I net anywhere between 25 and 45k in gold drops on these runs and anywhere from 6-9 rares.
Build
Barbarian - Game Guide - Diablo III
You could really use anything you are comfortable with. I like this build because I am used to it even though I know there are better out there.
Gear
Currently I am using all A1 Inferno gear with the exception of my weapon and shield. When I started these I was using A4 Hell gear and it wasn't that much more difficult.
9400dps (Base)
228 Resist All (341 with Warcry)
6915 Armor (8021 with Warcry)
46000 Health
44% Magic Find (No Neph)
5% Gold Find (No Neph)