Found a bug with this quest this morning. Or at least with one version of it. The quest objective text told me to go to Baandari Tradepost to give the goods to the client, but when I hit "show on map" it showed me Rawl'kha, with a quest marker there. As I've given her the goods in Rawl'kha before I figured the objective text was wrong, and I went to Rawl'kha. The quest marker showed up on my compass, but nobody was there. I checked the map for Malabal Tor to see if a quest marker showed up in Baandari Tradepost, but there was nothing there. I went there anyway, and about 30 seconds after wayshrining in the quest marker and the Countess suddenly appeared.

Practice getting away from the guards by doing the quest where you select FLEE and manage to get away, to the outlaw hideout. Craglorn is very good for this kind of practice. Just catch the guard on the way to/from the bank, then after you flee and start running cast a Retreating Maneuver spell, and keep running to the hideout back door, past the apple orchard, jump off the cliff into the river.

The Countess quests are the preferred ones from the tip board - you just need to deliver the goods once you have accumulated a bunch of laundered items from Heists or other sources, including rewards from previous Countess quests. It's worth laundering a few (white) stolen goods if they are the same types as others that you already have laundered. This works best if you already have maxed inventory (bag) space, including horse capacity. Ok to sell stolen goods if you already have a pile of the same type (e.g. "Dry Goods").

Important tip: save lots of Toys and Games, Cosmetics, Drinkware, Utensils and so on for when you do Clockwork City - the Crow dailies (enabled near the end of the main quest line) require a lot of these goods - either laundered or still stolen.

If you still need to acquire enough goods for this quest, the first place i always go is the west docks of Daggerfall City in Glenumbra. There are two ships with no-one inside. Steal everything that isn't nailed down if you still need to level up Legerdemain (launder the food items), or just ignore all the armor and food items if you only need gold and stolen items. Remember that you can also get stolen goods from bags and crates that normally give food items, you don't need to only hit the cabinets and backpacks etc.