What variety of green beans make the best pickled green beans?
The tradition has been to use the Blue Lake variety for canning and pickling, even though Kentucky Wonder is judged as having a fuller flavor.  One has to be careful with Blue Lake, as it is being bread for easy mechanical harvesting, with less attention being paid to flavor, according to the UCSC Agrecology Center.

When I grow stuff, I buy my seeds from Burpee.  The customer favorites list for snap peas (what they are now calling string beans, as the string is gone in many varieties) lists a stringless cross between Blue Lake and Kentucky.  That would be my choice for a pickle.  I would try to grow them slowly by not overwatering, as that increases the calcium content of the plant and how well the beans keep their texture submerged in a jar.