Given the size of Black Betha, Davos would have prioritized goods of a high value to size ratio. His former master Roro Uhoris, for example, sold weapons to the wildlings in exchange for furs, ivory, amber, and obsidian (and got hanged for it). From his conversation with Salladhor Saan, Davos used to specialize in smuggling spices and silks from Braavos, Myr, and Volantis, which fit the bill as being both very valuable and relatively compact. 

As most royal taxes are excise taxes of some kind and there is a pretty substantial bureaucracy of harbormasters, customs sergeants, factors, etc. there is an active black market and a small industry of men like Davos Seaworth and his former master who evade them for a profit. In terms of who backed him, Davos used to work with Salladhor Saan, for example.

Davos went to Storm’s End of his own accord.