I have to ask the question. Why go to such trouble to trap finches? To sell? To breed? To trade? To cage? To eat?
All of the above. (Except eat)
Remember when I told you about how it works with Gypsies and horses? Well the relationship with birds works along similar lines.Their value virtually non existant, except in the eye of another Gypsy. This time though, money isn't so important, it's more about bragging rights.
Again as with horses, there are certain characteristics that a Gypsy would look for in a good goldfinch.


Size: The bigger (Especially longer) the better.
Colour: Bright, well defined colours with bold clear lines of demarcation / separation.
A goldfinch blaze should be a vivid blood red and it should appear as square as possible, like a handkerchief draped over his head. (Not so in example above) In a cock bird, the blaze should extend beyond the eye.
The yellow (Buttercup yellow) wing bars should again be vivid and well defined.
The brown part should be nice and even and make him look like he is wearing a waistcoat and the white "Buttons" on his wings and tail should be big and symmetrical.
In addition to his size, shape and colour, there are other very important factors to consider.
Song: Cocks only) A good bird will sing almost continuously. Put his cage outside in the sunshine and he should really go to town. But it's very important that his song should consist of all goldfinch notes. (Goldfinches reared with canaries often pick up canary song which they incorporate into their own which spoils the song)
Temperament: He should be steady and confident. There is nothing worse that a goldfinch that flaps about all over the place in fear as soon as someone puts their face to the cage to look at him.
Calling: Cocks and hens) Sometimes when you are catching birds, one of the methods is to use a "Call bird" to lure passing birds into your net, or on to your lime. A good call bird will call so strongly that passing birds seem almost unable to resist.
Breeding: (Cocks only) Gypsies like to cross goldfinches with canaries to create goldfinch "Mules" Some goldfinch cocks are not only keen to tred any hen you put in front of them, they are also very fertile. In other words, they are good "Egg fillers"
So that's a very brief and superficial answer to part of your question.
More later.