Unfortunately I don't think there is a definite way to ensure one market gets an item. The best you can hope for is to put a warehouse near a market and have it only accept certain items and other warehouses not accept those items. The market buyers will go to any warehouse that has the item of interest - not just to the closest one. However, the market ladies also compete with each other sometimes in the sense that where there are two markets, one close and one far from the warehouse, who both need the same item, the one who's closer almost always gets the item first and the farther one never does and sometimes turns back when the stockpile of the item is zero.

The trade centre is where imports are dropped off. You can designate any warehouse to be the trade centre. If the trade centre is full (or doesn't accept that item), imports get taken to the warehouse closest to the centre that accepts that item. Any item in any warehouse can be exported if there is a trade route for it. However, the closer your import/exports warehouses are to the docks, the more efficiently they operate and the quicker they turn ships around. So it is not a necessity to have the trade centre and extra warehouses near the docks, but it is a benefit.