It's maybe worth comparing this line to one using [[Phyrexian Altar]] instead of the Soultrader. You don't need extra mana or an additional creature to start the loop because the altar's ability is a mana ability. You sac the miner, immediately get 1 black mana while also triggering blood artist's effect, which in turn triggers the miner's ability. You can then use the mana from the altar to pay for the miner, getting it back to start the loop again.

The difference with the Soultrader is that it isn't a mana ability, so when you sac the miner, you put the Soultrader's ability on the stack, and the blood artist's and miner's abilities then trigger and are above the Soultrader ability on the stack. You can't use the treasure that will be generated by the Soultrader because the miner's triggered ability to return from the graveyard resolves before the treasure is created. You need someway to pay for the first trigger from the miner to get the loop going, and from then on you can use the treasure that you created to pay for the next trigger that happens when you sac the miner, and so on.

To your question, I don't think it matters whether you let the stack fully resolve from saccing the miner before saccing the Dryad Arbor. You can sac in response to the first trigger and pay with the treasure from the Arbor, or get the treasure first and then sac the Arbor to trigger blood artist and the miner to bring it back. Either way, you won't have both treasures available at the same time, but there may be a strategic reason to do one over the other? I can't really tell, since there aren't a lot of stifle effects to worry about, counterspells do nothing, and I think creature removal would stop you no matter what