The Congratulations Crane or the Kotobukizuru is a variation of the traditional crane and is also a traditional design. It is a Japan custom to fold these cranes when congratulations are in order, such as a wedding.
It isn't exactly easy to make but it isn't too complicated either. And though it is a traditional design, it isn't a very common one that we see in origami books. So it is a different design to try out and is bound to garner more interest than the traditional peace crane.
The Congratulations Crane is described in the book 'Essential Origami' by Steve and Megumi Biddle. The same crane is also described in the blog 'Origami Weekly', although there it is described as 'Hiroshima Crane'.
The only difference between the 2 cranes is in the way you arrive at Step 16 of the crane described in 'Origami Weekly' (Step 11 in 'Essential Origami'). Whereas 'Origami Weekly' describes steps including a sink and a couple of inside-out turns, the steps described in 'Essential Origami' are simpler to do. From then onwards, both the instructions are the same.
As for the paper to be used, origami washi paper is the best fit for this model since the squashes require paper that does not tear easily.
Model Details:
Model: Congratulations Crane
Origin: Traditional
Book: Essential Origami
Authors: Steve and Megumi Biddle
Difficulty Level: Low Intermediate
Paper Ratio: Square
Paper Size: 6 inch squares
Tutorial: Youtube
Diagram: Origami Weekly