1/4" should be fine if you do not mind creating a lip around the op to act as a bracer. As a reference, I am making a 72" x 20" x 20" this weekend out of 1/4".
The adhesive cannot be purchased online, I don't think, as there are shipping restrictions on it. However, there are local places that sell it depending on your location - one off hand is near Quebec and I-70 (near the Port plastics I mentioned) and the other is near a LFS - Keys I think.
Shawn