I am down to selecting an interventional radiologist with experience or a vascular surgeon with experience to treat varicose veins. whom to choose?

Depends: I think if you gave a better idea regarding your location it can help with the suggestion of a surgeon.

Depends On Therapy: That depends on what type of treatment you need. The benefit of a vascular surgeon is that they can offer ALL possible treatment options, ranging from complex surgeries (such as vein ligations, vein stripping, phlebectomies, etc) to the less invasive options of endovenous laser ablation or sclerotherapy. Radiologist may be limited in what he can offer. Surgeons have done 7 yrs of surgery training.

Vein Specialist: There are many specialities which overlap in treating veins. I would recommend that you see someone who is certified by the American Board of Venous and Lymphatic Medicine. This is the board to certify Vein Specialists and anyone certified by this board is considered an expert in vein treatment.