You can build a key for sorted from two elements of your list items: (price, -count)(minus the score is used to invert the direction - more value will be the first as a result):
t = [('1', 3.0, 6), ('2', 2.0, 2), ('3', 2.0, 5), ('4', 4.0, 2), ('5', 2.0, 5),
('6', 3.0, 6), ('7', 3.0, 5), ('8', 2.0, 5), ('9', 3.0, 5), ('10', 3.0, 5)]
>>> sorted(t, key=lambda i: (i[1], -i[2]))
[('3', 2.0, 5), ('5', 2.0, 5), ('8', 2.0, 5), ('2', 2.0, 2), ('1', 3.0, 6),
('6', 3.0, 6), ('7', 3.0, 5), ('9', 3.0, 5), ('10', 3.0, 5), ('4', 4.0, 2)]
, min , :
>>> min(t, key=lambda i: (i[1], -i[2]))
('3', 2.0, 5)